메뉴 건너뛰기




Volumn , Issue , 2009, Pages 1-480

Combinatorics of compositions and words

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85055836007     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book
Times cited : (154)

References (194)
  • 1
    • 49549146613 scopus 로고
    • Enumeration of sequences by levels and rises
    • M. Abramson. Enumeration of sequences by levels and rises. Discrete Math., 12:101–112, 1975.
    • (1975) Discrete Math , vol.12 , pp. 101-112
    • Abramson, M.1
  • 2
    • 84894062635 scopus 로고
    • Restricted combinations and compositions
    • M. Abramson. Restricted combinations and compositions. Fibonacci Quart., 14(5):439–452, 1976.
    • (1976) Fibonacci Quart , vol.14 , Issue.5 , pp. 439-452
    • Abramson, M.1
  • 3
    • 0034557471 scopus 로고    scopus 로고
    • N-colour compositions
    • A.K. Agarwal. n-colour compositions. Indian J. Pure Appl. Math., 31(11):1421–1427, 2000.
    • (2000) Indian J. Pure Appl. Math. , vol.31 , Issue.11 , pp. 1421-1427
    • Agarwal, A.K.1
  • 4
    • 0142166943 scopus 로고    scopus 로고
    • An analogue of Euler’s identity and new combinatorial properties of n-colour compositions
    • A.K. Agarwal. An analogue of Euler’s identity and new combinatorial properties of n-colour compositions. J. Comput. Appl. Math., 160:9–15, 2003.
    • (2003) J. Comput. Appl. Math. , vol.160 , pp. 9-15
    • Agarwal, A.K.1
  • 5
    • 0004199721 scopus 로고
    • McGraw-Hill Book Co., New York, third edition
    • L.V. Ahlfors. Complex Analysis. McGraw-Hill Book Co., New York, third edition, 1978.
    • (1978) Complex Analysis
    • Ahlfors, L.V.1
  • 7
    • 0242364836 scopus 로고
    • Compositions with ones and twos
    • K. Alladi and V.E. Hoggatt, Jr. Compositions with ones and twos. Fibonacci Quart., 13(3):233–239, 1975.
    • (1975) Fibonacci Quart. , vol.13 , Issue.3 , pp. 233-239
    • Alladi, K.1    Hoggatt, V.E.2
  • 9
    • 0142254784 scopus 로고
    • Ramanujan’s “lost” notebook. IV. Stacks and alternating parity in partitions
    • G.E. Andrews. Ramanujan’s “lost” notebook. IV. Stacks and alternating parity in partitions. Adv. in Math., 53(1):55–74, 1984.
    • (1984) Adv. in Math. , vol.53 , Issue.1 , pp. 55-74
    • Andrews, G.E.1
  • 12
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • J. Baik, P. Deift, and K. Johansson. On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc., 12(4):1119–1178, 1999.
    • (1999) J. Amer. Math. Soc. , vol.12 , Issue.4 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 16
  • 17
    • 85055808099 scopus 로고    scopus 로고
    • ECO-generation for compositions and their restrictions
    • J.-L. Baril and P.-T. Do. ECO-generation for compositions and their restrictions. Proceedings of PP’08, 2008.
    • (2008) Proceedings of PP’08
    • Baril, J.-L.1    Do, P.-T.2
  • 18
    • 0015896876 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration
    • E.A. Bender. Central and local limit theorems applied to asymptotic enumeration. J. Combin. Theory Ser. A, 15:91–111, 1973.
    • (1973) J. Combin. Theory Ser. A , vol.15 , pp. 91-111
    • Bender, E.A.1
  • 19
    • 27844536560 scopus 로고    scopus 로고
    • Locally restricted compositions. I. Restricted adjacent differences
    • E.A. Bender and E.R. Canfield. Locally restricted compositions. I. Restricted adjacent differences. Electron.J.Combin., 12:#R57, 2005.
    • (2005) Electron.J.Combin. , vol.12 , pp. R57
    • Bender, E.A.1    Canfield, E.R.2
  • 20
    • 70349444747 scopus 로고    scopus 로고
    • Irreducible compositions and the first return to the origin of a random walk
    • E.A. Bender, G.F. Lawler, R. Pemantle, and H.S. Wilf. Irreducible compositions and the first return to the origin of a random walk. Sém. Lothar. Combin., 50:Art. B50h, 2003/04.
    • (2003) Sém. Lothar. Combin. , vol.50
    • Bender, E.A.1    Lawler, G.F.2    Pemantle, R.3    Wilf, H.S.4
  • 21
    • 0001183529 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration. II. multivariate generating functions
    • E.A. Bender and L.B. Richmond. Central and local limit theorems applied to asymptotic enumeration. II. multivariate generating functions. J. Combin. Theory Ser. A, 34(3):255–265, 1983.
    • (1983) J. Combin. Theory Ser. A , vol.34 , Issue.3 , pp. 255-265
    • Bender, E.A.1    Richmond, L.B.2
  • 27
    • 15844364569 scopus 로고    scopus 로고
    • Finite automata and pattern avoidance in words
    • P. Brändén and T. Mansour. Finite automata and pattern avoidance in words. J. Combin. Theory Ser. A, 110(1):127–145, 2005.
    • (2005) J. Combin. Theory Ser. A , vol.110 , Issue.1 , pp. 127-145
    • Brändén, P.1    Mansour, T.2
  • 28
    • 67649277745 scopus 로고    scopus 로고
    • The distribution of ascents of size d or more in compositions
    • C. Brennan and A. Knopfmacher. The distribution of ascents of size d or more in compositions. Discrete Math. Theor. Comput. Sci., 11(1):1–10, 2009.
    • (2009) Discrete Math. Theor. Comput. Sci. , vol.11 , Issue.1 , pp. 1-10
    • Brennan, C.1    Knopfmacher, A.2
  • 30
    • 33947395236 scopus 로고
    • Finding the recurrence relation for tiling 2 × n rectangles
    • R.C. Brigham, P.Z. Chinn, L.M. Holt, and R.S. Wilson. Finding the recurrence relation for tiling 2 × n rectangles. Congr. Numer., 105:134– 138, 1994.
    • (1994) Congr. Numer. , vol.105 , pp. 134-138
    • Brigham, R.C.1    Chinn, P.Z.2    Holt, L.M.3    Wilson, R.S.4
  • 33
    • 3042536898 scopus 로고    scopus 로고
    • Words restricted by patterns with at most 2 distinct letters
    • 03
    • A. Burstein and T. Mansour. Words restricted by patterns with at most 2 distinct letters. Electron.J.Combin., 9(2):#R3, 2002/03.
    • (2002) Electron.J.Combin. , vol.9 , Issue.2 , pp. R3
    • Burstein, A.1    Mansour, T.2
  • 35
    • 21244499125 scopus 로고    scopus 로고
    • Words restricted by 3-letter generalized multipermutation patterns
    • A. Burstein and T. Mansour. Words restricted by 3-letter generalized multipermutation patterns. Ann. Comb., 7(1):1–14, 2003.
    • (2003) Ann. Comb. , vol.7 , Issue.1 , pp. 1-14
    • Burstein, A.1    Mansour, T.2
  • 36
    • 84972547689 scopus 로고
    • Enumeration of sequences by rises and falls: A refinement of the Simon Newcomb problem
    • L. Carlitz. Enumeration of sequences by rises and falls: a refinement of the Simon Newcomb problem. Duke Math. J., 39:267–280, 1972.
    • (1972) Duke Math. J. , vol.39 , pp. 267-280
    • Carlitz, L.1
  • 37
    • 33846847097 scopus 로고
    • Enumeration of up-down sequences
    • L. Carlitz. Enumeration of up-down sequences. Discrete Math., 4:273– 286, 1973.
    • (1973) Discrete Math , vol.4 , pp. 273-286
    • Carlitz, L.1
  • 38
    • 0007584478 scopus 로고
    • Restricted compositions
    • L. Carlitz. Restricted compositions. Fibonacci Quart., 14(3):254–264, 1976.
    • (1976) Fibonacci Quart , vol.14 , Issue.3 , pp. 254-264
    • Carlitz, L.1
  • 39
    • 84985330904 scopus 로고
    • Enumeration of compositions by rises, falls and levels
    • L. Carlitz. Enumeration of compositions by rises, falls and levels. Math. Nachr., 77:361–371, 1977.
    • (1977) Math. Nachr. , vol.77 , pp. 361-371
    • Carlitz, L.1
  • 40
    • 85055793179 scopus 로고
    • In Studies in foundations and combinatorics, volume 1 of Adv
    • Academic Press, New York
    • L. Carlitz. Up-down and down-up partitions. In Studies in foundations and combinatorics, volume 1 of Adv. in Math. Suppl. Stud., pages 101– 129. Academic Press, New York, 1978.
    • (1978) Math. Suppl. Stud. , pp. 101-129
    • Up-Down, L.C.1    Partitions, D.-U.2
  • 42
    • 0000752989 scopus 로고
    • Enumeration of pairs of sequences by rises, falls and levels
    • L. Carlitz, R. Scoville, and T. Vaughan. Enumeration of pairs of sequences by rises, falls and levels. Manuscripta Math., 19(3):211–243, 1976.
    • (1976) Manuscripta Math , vol.19 , Issue.3 , pp. 211-243
    • Carlitz, L.1    Scoville, R.2    Vaughan, T.3
  • 43
    • 49549154846 scopus 로고
    • Enumeration of sequences of given specification according to rises, falls and maxima
    • L. Carlitz and T. Vaughan. Enumeration of sequences of given specification according to rises, falls and maxima. Discrete Math., 8:147–167, 1974.
    • (1974) Discrete Math , vol.8 , pp. 147-167
    • Carlitz, L.1    Vaughan, T.2
  • 45
    • 49049139125 scopus 로고
    • Enumeration of compositions with prescribed parts
    • M. Cerasoli. Enumeration of compositions with prescribed parts. J. Math. Anal. Appl., 89(2):351–358, 1982.
    • (1982) J. Math. Anal. Appl. , vol.89 , Issue.2 , pp. 351-358
    • Cerasoli, M.1
  • 46
    • 0007888247 scopus 로고
    • On the enumeration of certain compositions and related sequences of numbers
    • Ch.A. Charalambides. On the enumeration of certain compositions and related sequences of numbers. Fibonacci Quart., 20(2):132–146, 1982.
    • (1982) Fibonacci Quart , vol.20 , Issue.2 , pp. 132-146
    • Charalambides, C.A.1
  • 48
    • 0242350473 scopus 로고    scopus 로고
    • The frequency of summands of a particular size in palindromic compositions
    • P. Chinn, R.P. Grimaldi, and S. Heubach. The frequency of summands of a particular size in palindromic compositions. Ars Combin., 69:65–78, 2003.
    • (2003) Ars Combin , vol.69 , pp. 65-78
    • Chinn, P.1    Grimaldi, R.P.2    Heubach, S.3
  • 50
    • 84880062392 scopus 로고    scopus 로고
    • (1, k)-compositions
    • P. Chinn and S. Heubach. (1, k)-compositions. Congr. Numer., 164:183– 194, 2003.
    • (2003) Congr. Numer. , vol.164 , pp. 183-194
    • Chinn, P.1    Heubach, S.2
  • 51
    • 65249151685 scopus 로고    scopus 로고
    • Compositions of n with no occurrence of k
    • P. Chinn and S. Heubach. Compositions of n with no occurrence of k. Congr. Numer., 164:33–51, 2003.
    • (2003) Congr. Numer. , vol.164 , pp. 33-51
    • Chinn, P.1    Heubach, S.2
  • 52
    • 2942711429 scopus 로고    scopus 로고
    • Integer sequences related to compositions without 2’s
    • P. Chinn and S. Heubach. Integer sequences related to compositions without 2’s. J. Integer Seq., 6(2):Art. 03.2.3, 2003.
    • (2003) J. Integer Seq. , vol.6 , Issue.2
    • Chinn, P.1    Heubach, S.2
  • 53
    • 0000073312 scopus 로고    scopus 로고
    • Forbidden subsequences and Chebyshev polynomials
    • T. Chow and J. West. Forbidden subsequences and Chebyshev polynomials. Discrete Math., 204(1-3):119–128, 1999.
    • (1999) Discrete Math , vol.204 , Issue.1-3 , pp. 119-128
    • Chow, T.1    West, J.2
  • 55
    • 0035642626 scopus 로고    scopus 로고
    • Generalized pattern avoidance
    • A. Claesson. Generalized pattern avoidance. European J. Combin., 22(7):961–971, 2001.
    • (2001) European J. Combin. , vol.22 , Issue.7 , pp. 961-971
    • Claesson, A.1
  • 56
    • 9144268939 scopus 로고    scopus 로고
    • Partitions and compositions defined by inequalities
    • S. Corteel and C.D. Savage. Partitions and compositions defined by inequalities. Ramanujan J., 8(3):357–381, 2004.
    • (2004) Ramanujan J , vol.8 , Issue.3 , pp. 357-381
    • Corteel, S.1    Savage, C.D.2
  • 57
    • 63149128933 scopus 로고    scopus 로고
    • A note on partitions and compositions defined by inequalities
    • S. Corteel, C.D. Savage, and H.S. Wilf. A note on partitions and compositions defined by inequalities. Integers, 5(1):A24, 2005.
    • (2005) Integers , vol.5 , Issue.1 , pp. A24
    • Corteel, S.1    Savage, C.D.2    Wilf, H.S.3
  • 58
    • 33847282960 scopus 로고    scopus 로고
    • K-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams
    • A. de Mier. k-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams. Electron. Notes Discrete Math., 28:3–10, 2007.
    • (2007) Electron. Notes Discrete Math. , vol.28 , pp. 3-10
    • de Mier, A.1
  • 61
    • 33750472293 scopus 로고    scopus 로고
    • Words avoiding a reflexive acyclic relation
    • J. Dollhopf, I. Goulden, and C. Greene. Words avoiding a reflexive acyclic relation. Electron. J. Combin., 11(2):#R28, 2004/06.
    • (2004) Electron. J. Combin. , vol.11 , Issue.2 , pp. R28
    • Dollhopf, J.1    Goulden, I.2    Greene, C.3
  • 62
    • 3042517902 scopus 로고
    • The length of a supersequence for a set of binary words with a given number of units
    • A.A. Evdokimov and V. Nyu. The length of a supersequence for a set of binary words with a given number of units. Metody Diskret. Anal., 52:49–58, 1992.
    • (1992) Metody Diskret. Anal. , vol.52 , pp. 49-58
    • Evdokimov, A.A.1    Nyu, V.2
  • 63
    • 0037014241 scopus 로고    scopus 로고
    • An algebraic characterization of the set of succession rules
    • L. Ferrari, E. Pergola, R. Pinzani, and S. Rinaldi. An algebraic characterization of the set of succession rules. Theoret. Comput. Sci., 281(1-2):351–367, 2002.
    • (2002) Theoret. Comput. Sci. , vol.281 , Issue.1-2 , pp. 351-367
    • Ferrari, L.1    Pergola, E.2    Pinzani, R.3    Rinaldi, S.4
  • 64
    • 33744775944 scopus 로고    scopus 로고
    • Three-letter-pattern-avoiding permutations and functional equations
    • G. Firro and T. Mansour. Three-letter-pattern-avoiding permutations and functional equations. Electron.J.Combin., 13(1):#R51, 2006.
    • (2006) Electron.J.Combin. , vol.13 , Issue.1 , pp. R51
    • Firro, G.1    Mansour, T.2
  • 65
    • 59749095617 scopus 로고    scopus 로고
    • Restricted k-ary words and functional equations
    • G. Firro and T. Mansour. Restricted k-ary words and functional equations. Discrete Appl. Math., 157(4):602–616, 2009.
    • (2009) Discrete Appl. Math. , vol.157 , Issue.4 , pp. 602-616
    • Firro, G.1    Mansour, T.2
  • 66
    • 0001566238 scopus 로고
    • Statistical mechanics of dimers on a plane lattice
    • M.E. Fisher. Statistical mechanics of dimers on a plane lattice. Phys. Rev. (2), 124:1664–1672, 1961.
    • (1961) Phys. Rev. , vol.124 , Issue.2 , pp. 1664-1672
    • Fisher, M.E.1
  • 67
    • 0029326388 scopus 로고
    • Mellin transforms and asymptotics: Harmonic sums
    • P. Flajolet, X. Gourdon, and P. Dumas. Mellin transforms and asymptotics: harmonic sums. Theoret. Comput. Sci., 144(1-2):3–58, 1995.
    • (1995) Theoret. Comput. Sci. , vol.144 , Issue.1-2 , pp. 3-58
    • Flajolet, P.1    Gourdon, X.2    Dumas, P.3
  • 69
    • 0002235458 scopus 로고
    • Direct calculation of k-generalized Fibonacci numbers
    • I. Flores. Direct calculation of k-generalized Fibonacci numbers. Fibonacci Quart., 5:259–266, 1967.
    • (1967) Fibonacci Quart , vol.5 , pp. 259-266
    • Flores, I.1
  • 71
    • 11544370840 scopus 로고    scopus 로고
    • Transformations on words
    • D. Foata and G.-N. Han. Transformations on words. J. Algorithms, 28(1):172–191, 1998.
    • (1998) J. Algorithms , vol.28 , Issue.1 , pp. 172-191
    • Foata, D.1    Han, G.-N.2
  • 73
    • 0036375704 scopus 로고    scopus 로고
    • Average number of distinct part sizes in a random Carlitz composition
    • W.M.Y. Goh and P. Hitczenko. Average number of distinct part sizes in a random Carlitz composition. European J. Combin., 23(6):647–657, 2002.
    • (2002) European J. Combin. , vol.23 , Issue.6 , pp. 647-657
    • Goh, W.M.Y.1    Hitczenko, P.2
  • 74
    • 0009312236 scopus 로고
    • Binomial coefficients, the bracket function, and compositions with relatively prime summands
    • H.W. Gould. Binomial coefficients, the bracket function, and compositions with relatively prime summands. Fibonacci Quart., 2:241–260, 1964.
    • (1964) Fibonacci Quart , vol.2 , pp. 241-260
    • Gould, H.W.1
  • 76
    • 0242301792 scopus 로고    scopus 로고
    • Compositions with odd summands
    • R.P. Grimaldi. Compositions with odd summands. Congr. Numer., 142:113–127, 2000.
    • (2000) Congr. Numer. , vol.142 , pp. 113-127
    • Grimaldi, R.P.1
  • 77
    • 2942733744 scopus 로고    scopus 로고
    • Compositions without the summand 1
    • R.P. Grimaldi. Compositions without the summand 1. Congr. Numer., 152:33–43, 2001.
    • (2001) Congr. Numer. , vol.152 , pp. 33-43
    • Grimaldi, R.P.1
  • 79
    • 77955526044 scopus 로고    scopus 로고
    • Compositions and the alternate Fibonacci numbers
    • R.P. Grimaldi. Compositions and the alternate Fibonacci numbers. Congr. Numer., 186:81–96, 2007.
    • (2007) Congr. Numer. , vol.186 , pp. 81-96
    • Grimaldi, R.P.1
  • 82
    • 0013199946 scopus 로고    scopus 로고
    • Enumeration of tilings of diamonds and hexagons with defects
    • H.A. Helfgott and I.M. Gessel. Enumeration of tilings of diamonds and hexagons with defects. Electron.J.Combin., 6:#R16, 1999.
    • (1999) Electron.J.Combin , vol.6 , pp. R16
    • Helfgott, H.A.1    Gessel, I.M.2
  • 84
    • 0142191744 scopus 로고    scopus 로고
    • Tiling an m-by-n area with squares of size up to k-by-k (M ≤ 5)
    • S. Heubach. Tiling an m-by-n area with squares of size up to k-by-k (m ≤ 5). Congr. Numer., 140:43–64, 1999.
    • (1999) Congr. Numer. , vol.140 , pp. 43-64
    • Heubach, S.1
  • 85
    • 33947354567 scopus 로고    scopus 로고
    • Patterns arising from tiling rectangles with 1-by-1 and 2-by-2 squares
    • S. Heubach and P. Chinn. Patterns arising from tiling rectangles with 1-by-1 and 2-by-2 squares. Congr. Numer., 150:173–192, 2001.
    • (2001) Congr. Numer. , vol.150 , pp. 173-192
    • Heubach, S.1    Chinn, P.2
  • 87
    • 0242426730 scopus 로고    scopus 로고
    • Rises, levels, drops and “+” signs in compositions: Extensions of a paper by Alladi and Hoggatt
    • S. Heubach, P. Chinn, and R.P. Grimaldi. Rises, levels, drops and “+” signs in compositions: extensions of a paper by Alladi and Hoggatt. Fibonacci Quart., 41(3):229–239, 2003.
    • (2003) Fibonacci Quart , vol.41 , Issue.3 , pp. 229-239
    • Heubach, S.1    Chinn, P.2    Grimaldi, R.P.3
  • 88
    • 70349508317 scopus 로고    scopus 로고
    • Partially ordered patterns in compositions
    • S. Heubach, S. Kitaev, and T. Mansour. Partially ordered patterns in compositions. Pure Math. Appl., 17(1-2):123–134, 2006.
    • (2006) Pure Math. Appl. , vol.17 , Issue.1-2 , pp. 123-134
    • Heubach, S.1    Kitaev, S.2    Mansour, T.3
  • 89
    • 65249097549 scopus 로고    scopus 로고
    • Compositions of n with parts in a set
    • S. Heubach and T. Mansour. Compositions of n with parts in a set. Congr. Numer., 168:127–143, 2004.
    • (2004) Congr. Numer. , vol.168 , pp. 127-143
    • Heubach, S.1    Mansour, T.2
  • 90
    • 31544477240 scopus 로고    scopus 로고
    • Counting rises, levels, and drops in compositions
    • S. Heubach and T. Mansour. Counting rises, levels, and drops in compositions. Integers, 5(1):A11, 2005.
    • (2005) Integers , vol.5 , Issue.1 , pp. A11
    • Heubach, S.1    Mansour, T.2
  • 91
    • 31544436897 scopus 로고    scopus 로고
    • Avoiding patterns of length three in compositions and multiset permutations
    • S. Heubach and T. Mansour. Avoiding patterns of length three in compositions and multiset permutations. Adv. in Appl. Math., 36(2):156– 174, 2006.
    • (2006) Adv. in Appl. Math. , vol.36 , Issue.2 , pp. 156-174
    • Heubach, S.1    Mansour, T.2
  • 92
    • 77949423394 scopus 로고    scopus 로고
    • Enumeration of 3-letter patterns in compositions
    • deGruyter
    • S. Heubach and T. Mansour. Enumeration of 3-letter patterns in compositions. In Combinatorial Number Theory, pages 243–264. deGruyter, 2007.
    • (2007) In Combinatorial Number Theory , pp. 243-264
    • Heubach, S.1    Mansour, T.2
  • 93
    • 0035539871 scopus 로고    scopus 로고
    • Distinctness of compositions of an integer: A probabilistic analysis
    • P. Hitczenko and G. Louchard. Distinctness of compositions of an integer: a probabilistic analysis. Random Structures Algorithms, 19(3-4):407–437, 2001.
    • (2001) Random Structures Algorithms , vol.19 , Issue.3-4 , pp. 407-437
    • Hitczenko, P.1    Louchard, G.2
  • 94
    • 0036566404 scopus 로고    scopus 로고
    • A generatingfunctionology approach to a problem of Wilf
    • P. Hitczenko, C. Rousseau, and C.D. Savage. A generatingfunctionology approach to a problem of Wilf. J. Comput. Appl. Math., 142:107–114, 2002.
    • (2002) J. Comput. Appl. Math. , vol.142 , pp. 107-114
    • Hitczenko, P.1    Rousseau, C.2    Savage, C.D.3
  • 95
    • 84874971400 scopus 로고    scopus 로고
    • On the probability that a randomly chosen part size in a random composition is unrepeated
    • János Bolyai Math. Soc., Budapest
    • P. Hitczenko and C.D. Savage. On the probability that a randomly chosen part size in a random composition is unrepeated. In Paul Erdős and his mathematics (Budapest, 1999), pages 108–111. János Bolyai Math. Soc., Budapest, 1999.
    • (1999) Paul Erdős and His Mathematics (Budapest, 1999) , pp. 108-111
    • Hitczenko, P.1    Savage, C.D.2
  • 96
    • 8344235198 scopus 로고    scopus 로고
    • On the multiplicity of parts in a random composition of a large integer
    • (electronic)
    • P. Hitczenko and C.D. Savage. On the multiplicity of parts in a random composition of a large integer. SIAM J. Discrete Math., 18(2):418–435 (electronic), 2004.
    • (1996) SIAM J. Discrete Math. , vol.18 , Issue.2 , pp. 418-435
    • Hitczenko, P.1    Savage, C.D.2
  • 97
    • 0034551055 scopus 로고    scopus 로고
    • Expected number of distinct part sizes in a random integer composition
    • P. Hitczenko and G. Stengle. Expected number of distinct part sizes in a random integer composition. Combin. Probab. Comput., 9(6):519–527, 2000.
    • (2000) Combin. Probab. Comput. , vol.9 , Issue.6 , pp. 519-527
    • Hitczenko, P.1    Stengle, G.2
  • 98
    • 70349625877 scopus 로고
    • Palindromic compositions
    • V.E. Hoggatt, Jr. and M. Bicknell. Palindromic compositions. Fibonacci Quart., 13(4):350–356, 1975.
    • (1975) Fibonacci Quart. , vol.13 , Issue.4 , pp. 350-356
    • Hoggatt, V.E.1    Bicknell, M.2
  • 99
    • 58149412155 scopus 로고
    • Fibonacci and binomial properties of weighted compositions
    • V.E. Hoggatt, Jr. and D.A. Lind. Fibonacci and binomial properties of weighted compositions. J. Combin. Theory Ser. A, 4:121–124, 1968.
    • (1968) J. Combin. Theory Ser. A , vol.4 , pp. 121-124
    • Hoggatt, V.E.1    Lind, D.A.2
  • 100
    • 4043127094 scopus 로고
    • Compositions and Fibonacci numbers
    • V.E. Hoggatt, Jr. and D.A. Lind. Compositions and Fibonacci numbers. Fibonacci Quart., 7(3):253–266, 1969.
    • (1969) Fibonacci Quart. , vol.7 , Issue.3 , pp. 253-266
    • Hoggatt, V.E.1    Lind, D.A.2
  • 102
    • 0001187704 scopus 로고    scopus 로고
    • Measures of distinctness for random partitions and compositions of an integer
    • H.-K. Hwang and Y.-N. Yeh. Measures of distinctness for random partitions and compositions of an integer. Adv. in Appl. Math., 19(3):378– 414, 1997.
    • (1997) Adv. in Appl. Math. , vol.19 , Issue.3 , pp. 378-414
    • Hwang, H.-K.1    Yeh, Y.-N.2
  • 103
    • 33645149332 scopus 로고    scopus 로고
    • Meta-Fibonacci sequences, binary trees and extremal compact codes
    • B. Jackson and F. Ruskey. Meta-Fibonacci sequences, binary trees and extremal compact codes. Electron.J.Combin., 13(1):#R26, 2006.
    • (2006) Electron.J.Combin. , vol.13 , Issue.1 , pp. R26
    • Jackson, B.1    Ruskey, F.2
  • 104
    • 41549085018 scopus 로고    scopus 로고
    • On pattern-avoiding partitions
    • V. Jelínek and T. Mansour. On pattern-avoiding partitions. Electron. J. Combin., 15(1):#R39, 2008.
    • (2008) Electron. J. Combin. , vol.15 , Issue.1 , pp. R39
    • Jelínek, V.1    Mansour, T.2
  • 105
    • 67650704160 scopus 로고    scopus 로고
    • Wilf-equivalence on k-ary words, compositions, and parking functions
    • V. Jelínek and T. Mansour. Wilf-equivalence on k-ary words, compositions, and parking functions. Electron.J.Combin., 16(1):#R58, 2009.
    • (2009) Electron.J.Combin. , vol.16 , Issue.1 , pp. R58
    • Jelínek, V.1    Mansour, T.2
  • 106
    • 0038971757 scopus 로고    scopus 로고
    • Approximating the number of monomer-dimer coverings of a lattice
    • C. Kenyon, D. Randall, and A. Sinclair. Approximating the number of monomer-dimer coverings of a lattice. J. Statist. Phys., 83(3-4):637–659, 1996.
    • (1996) J. Statist. Phys. , vol.83 , Issue.3-4 , pp. 637-659
    • Kenyon, C.1    Randall, D.2    Sinclair, A.3
  • 108
    • 24144494606 scopus 로고    scopus 로고
    • Partially ordered generalized patterns
    • S. Kitaev. Partially ordered generalized patterns. Discrete Math., 298(1-3):212–229, 2005.
    • (2005) Discrete Math , vol.298 , Issue.1-3 , pp. 212-229
    • Kitaev, S.1
  • 109
    • 27844515628 scopus 로고    scopus 로고
    • Partially ordered generalized patterns and k-ary words
    • S. Kitaev and T. Mansour. Partially ordered generalized patterns and k-ary words. Ann. Comb., 7(2):191–200, 2003.
    • (2003) Ann. Comb. , vol.7 , Issue.2 , pp. 191-200
    • Kitaev, S.1    Mansour, T.2
  • 110
    • 49749083457 scopus 로고    scopus 로고
    • Counting descents, rises, and levels, with prescribed first element, in words
    • S. Kitaev, T. Mansour, and J.B. Remmel. Counting descents, rises, and levels, with prescribed first element, in words. Discrete Math. Theor. Comput. Sci., 10(3):1–22, 2008.
    • (2008) Discrete Math. Theor. Comput. Sci. , vol.10 , Issue.3 , pp. 1-22
    • Kitaev, S.1    Mansour, T.2    Remmel, J.B.3
  • 111
    • 70349497839 scopus 로고    scopus 로고
    • Enumerating segmented patterns in compositions and encoding by restricted permutations
    • S. Kitaev, T.B. McAllister, and T.K. Petersen. Enumerating segmented patterns in compositions and encoding by restricted permutations. Integers, 6:A34, 2006.
    • (2006) Integers , vol.6 , pp. A34
    • Kitaev, S.1    McAllister, T.B.2    Petersen, T.K.3
  • 112
    • 0030537090 scopus 로고    scopus 로고
    • On abab-free and abba-free set partitions
    • M. Klazar. On abab-free and abba-free set partitions. European J. Combin., 17(1):53–68, 1996.
    • (1996) European J. Combin. , vol.17 , Issue.1 , pp. 53-68
    • Klazar, M.1
  • 113
    • 0007161479 scopus 로고    scopus 로고
    • On trees and noncrossing partitions
    • M. Klazar. On trees and noncrossing partitions. Discrete Appl. Math., 82(1-3):263–269, 1998.
    • (1998) Discrete Appl. Math. , vol.82 , Issue.1-3 , pp. 263-269
    • Klazar, M.1
  • 117
    • 0040118790 scopus 로고    scopus 로고
    • Compositions with m distinct parts
    • A. Knopfmacher and M.E. Mays. Compositions with m distinct parts. Ars Combin., 53:111–128, 1999.
    • (1999) Ars Combin , vol.53 , pp. 111-128
    • Knopfmacher, A.1    Mays, M.E.2
  • 118
    • 85055851390 scopus 로고    scopus 로고
    • The sum of distinct parts in compositions and partitions
    • A. Knopfmacher and M.E. Mays. The sum of distinct parts in compositions and partitions. Bull.Inst.Combin.Appl., 25:66–78, 1999.
    • (1999) Bull.Inst.Combin.Appl. , vol.25 , pp. 66-78
    • Knopfmacher, A.1    Mays, M.E.2
  • 121
    • 33644700780 scopus 로고    scopus 로고
    • Compositions with parts constrained by the leading summand
    • A. Knopfmacher and N. Robbins. Compositions with parts constrained by the leading summand. Ars Combin., 76:287–295, 2005.
    • (2005) Ars Combin , vol.76 , pp. 287-295
    • Knopfmacher, A.1    Robbins, N.2
  • 122
    • 0003657590 scopus 로고
    • Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont
    • D.E. Knuth. The art of computer programming. Volume 3. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1973.
    • (1973) The Art of Computer Programming , vol.3
    • Knuth, D.E.1
  • 123
    • 0003657590 scopus 로고
    • Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, second edition
    • D.E. Knuth. The art of computer programming. Volume 1. Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, second edition, 1975.
    • (1975) The Art of Computer Programming. , vol.1
    • Knuth, D.E.1
  • 124
    • 0000906017 scopus 로고
    • The average time for carry propagation
    • D.E. Knuth. The average time for carry propagation. Nederl. Akad. Wetensch. Indag. Math., 40(2):238–242, 1978.
    • (1978) Nederl. Akad. Wetensch. Indag. Math. , vol.40 , Issue.2 , pp. 238-242
    • Knuth, D.E.1
  • 126
    • 0035413460 scopus 로고    scopus 로고
    • Permutations with restricted patterns and Dyck paths
    • C. Krattenthaler. Permutations with restricted patterns and Dyck paths. Adv. in Appl. Math., 27(2-3):510–530, 2001.
    • (2001) Adv. in Appl. Math. , vol.27 , Issue.2-3 , pp. 510-530
    • Krattenthaler, C.1
  • 127
    • 33747842788 scopus 로고    scopus 로고
    • Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes
    • C. Krattenthaler. Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes. Adv. in Appl. Math., 37(3):404–431, 2006.
    • (2006) Adv. in Appl. Math. , vol.37 , Issue.3 , pp. 404-431
    • Krattenthaler, C.1
  • 128
    • 0002099330 scopus 로고
    • Criterion for smoothness of Schubert varieties in Sl(N)/B
    • V. Lakshmibai and B. Sandhya. Criterion for smoothness of Schubert varieties in Sl(n)/B. Proc. Indian Acad. Sci. Math. Sci., 100(1):45–52, 1990.
    • (1990) Proc. Indian Acad. Sci. Math. Sci. , vol.100 , Issue.1 , pp. 45-52
    • Lakshmibai, V.1    Sandhya, B.2
  • 129
    • 0000472034 scopus 로고
    • D-finite power series
    • L. Lipshitz. D-finite power series. J. Algebra, 122(2):353–373, 1989.
    • (1989) J. Algebra , vol.122 , Issue.2 , pp. 353-373
    • Lipshitz, L.1
  • 133
    • 33645602530 scopus 로고    scopus 로고
    • The number of distinct part sizes of some multiplicity in compositions of an integer: A probabilistic analysis
    • Discrete Mathematics and Theoretical Computer Science
    • G. Louchard. The number of distinct part sizes of some multiplicity in compositions of an integer: A probabilistic analysis. In Random Walks, volume AC of DMTCS Proceedings, pages 155–170. Discrete Mathematics and Theoretical Computer Science, 2003.
    • (2003) Random Walks, Volume AC of DMTCS Proceedings , pp. 155-170
    • Louchard, G.1
  • 135
    • 84935872450 scopus 로고
    • Some group elements defined by commutators
    • I.D. MacDonald. Some group elements defined by commutators. Math. Sci., 4(2):129–131, 1979.
    • (1979) Math. Sci. , vol.4 , Issue.2 , pp. 129-131
    • Macdonald, I.D.1
  • 136
    • 34047256626 scopus 로고
    • Memoir on the theory of the compositions of numbers
    • P.A. MacMahon. Memoir on the theory of the compositions of numbers. Phil. Trans. Royal Society London. A, 184:835–901, 1893.
    • (1893) Phil. Trans. Royal Society London. A , vol.184 , pp. 835-901
    • Macmahon, P.A.1
  • 137
    • 0001023516 scopus 로고
    • The Indices of Permutations and the Derivation Therefrom of Functions of a Single Variable Associated with the Permutations of any Assemblage of Objects
    • P.A. MacMahon. The Indices of Permutations and the Derivation Therefrom of Functions of a Single Variable Associated with the Permutations of any Assemblage of Objects. Amer.J.Math., 35(3):281–322, 1913.
    • (1913) Amer.J.Math. , vol.35 , Issue.3 , pp. 281-322
    • Macmahon, P.A.1
  • 138
    • 0004205061 scopus 로고    scopus 로고
    • II (bound in one volume). Dover Phoenix Editions. Dover Publications Inc., Mineola, NY, Reprint of An introduction to combinatory analysis (1920) and Combinatory analysis
    • P.A. MacMahon. Combinatory analysis. Vol. I, II (bound in one volume). Dover Phoenix Editions. Dover Publications Inc., Mineola, NY, 2004. Reprint of An introduction to combinatory analysis (1920) and Combinatory analysis. Vol. I, II (1915, 1916).
    • (2004) Combinatory Analysis , vol.1
    • Macmahon, P.A.1
  • 139
    • 85055784288 scopus 로고    scopus 로고
    • T. Mansour. http://math.haifa.ac.il/toufik/automaton01.html. Automaton program, 2003.
    • (2003)
    • Mansour, T.1
  • 140
    • 85055854403 scopus 로고    scopus 로고
    • Table of values computed with automaton program
    • T. Mansour. http://math.haifa.ac.il/toufik/table4auto.html. Table of values computed with automaton program, 2003.
    • (2003)
    • Mansour, T.1
  • 141
    • 31544439892 scopus 로고    scopus 로고
    • Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions
    • T. Mansour. Restricted 132-avoiding k-ary words, Chebyshev polynomials, and continued fractions. Adv. in Appl. Math., 36(2):175–193, 2006.
    • (2006) Adv. in Appl. Math. , vol.36 , Issue.2 , pp. 175-193
    • Mansour, T.1
  • 142
    • 79251625020 scopus 로고    scopus 로고
    • Longest alternating subsequences in pattern-restricted kary words
    • T. Mansour. Longest alternating subsequences in pattern-restricted kary words. Online J. Analytic Combin., 3:#5, 2008.
    • (2008) Online J. Analytic Combin. , vol.3 , pp. 5
    • Mansour, T.1
  • 143
    • 35648937577 scopus 로고    scopus 로고
    • Longest alternating subsequences of k-ary words
    • T. Mansour. Longest alternating subsequences of k-ary words. Discrete Appl. Math., 156(1):119–124, 2008.
    • (2008) Discrete Appl. Math. , vol.156 , Issue.1 , pp. 119-124
    • Mansour, T.1
  • 147
    • 0037891640 scopus 로고    scopus 로고
    • Restricted 132-avoiding permutations
    • T. Mansour and A. Vainshtein. Restricted 132-avoiding permutations. Adv. in Appl. Math., 26(3):258–269, 2001.
    • (2001) Adv. in Appl. Math. , vol.26 , Issue.3 , pp. 258-269
    • Mansour, T.1    Vainshtein, A.2
  • 148
    • 0041907053 scopus 로고    scopus 로고
    • Restricted permutations and Chebyshev polynomials
    • T. Mansour and A. Vainshtein. Restricted permutations and Chebyshev polynomials. Sém. Lothar. Combin., 47:Art. B47c, 2001/02.
    • (2001) Sém. Lothar. Combin. , vol.47
    • Mansour, T.1    Vainshtein, A.2
  • 149
    • 0036225910 scopus 로고    scopus 로고
    • Counting occurrences of 132 in a permutation
    • T. Mansour and A. Vainshtein. Counting occurrences of 132 in a permutation. Adv. in Appl. Math., 28(2):185–195, 2002.
    • (2002) Adv. in Appl. Math. , vol.28 , Issue.2 , pp. 185-195
    • Mansour, T.1    Vainshtein, A.2
  • 151
    • 0042003737 scopus 로고
    • Exact recursion relation for 2 x n arrays of dumbbells
    • R.B. McQuistan and S.J. Lichtman. Exact recursion relation for 2 x n arrays of dumbbells. J. Math. Phy., 11(10):3095–3099, 1970.
    • (1970) J. Math. Phy. , vol.11 , Issue.10 , pp. 3095-3099
    • McQuistan, R.B.1    Lichtman, S.J.2
  • 154
    • 65249149981 scopus 로고    scopus 로고
    • A unified approach to the study of general and palindromic compositions
    • D. Merlini, F. Uncini, and M.C. Verri. A unified approach to the study of general and palindromic compositions. Integers, 4:A23, 2004.
    • (2004) Integers , vol.4 , pp. A23
    • Merlini, D.1    Uncini, F.2    Verri, M.C.3
  • 155
    • 84910199438 scopus 로고
    • Some properties of compositions and their application to the ballot problem
    • S.G. Mohanty. Some properties of compositions and their application to the ballot problem. Canad. Math. Bull., 8:359–372, 1965.
    • (1965) Canad. Math. Bull. , vol.8 , pp. 359-372
    • Mohanty, S.G.1
  • 156
    • 84910289837 scopus 로고
    • Restricted compositions
    • S.G. Mohanty. Restricted compositions. Fibonacci Quart., 5:223–234, 1967.
    • (1967) Fibonacci Quart , vol.5 , pp. 223-234
    • Mohanty, S.G.1
  • 157
    • 43149104411 scopus 로고    scopus 로고
    • Pattern avoidance in multiset permutations: Bijective proof
    • A.N. Myers. Pattern avoidance in multiset permutations: bijective proof. Ann. Comb., 11(3-4):507–517, 2007.
    • (2007) Ann. Comb. , vol.11 , Issue.3-4 , pp. 507-517
    • Myers, A.N.1
  • 158
    • 58449098547 scopus 로고    scopus 로고
    • Left-to-right maxima in words and multiset permutations
    • A.N. Myers and H.S. Wilf. Left-to-right maxima in words and multiset permutations. Israel J. Math., 166:167–183, 2008.
    • (2008) Israel J. Math. , vol.166 , pp. 167-183
    • Myers, A.N.1    Wilf, H.S.2
  • 160
    • 38949150789 scopus 로고    scopus 로고
    • Lattice paths and n-colour compositions
    • G. Narang and A.K. Agarwal. Lattice paths and n-colour compositions. Discrete Math., 308(9):1732–1740, 2008.
    • (2008) Discrete Math , vol.308 , Issue.9 , pp. 1732-1740
    • Narang, G.1    Agarwal, A.K.2
  • 161
    • 0000400951 scopus 로고
    • Sur les treillis formés par les partitions d’un entier et leurs applications àlathéorie des probabilités
    • T.V. Narayana. Sur les treillis formés par les partitions d’un entier et leurs applications àlathéorie des probabilités. C. R. Acad. Sci. Paris, 240:1188–1189, 1955.
    • (1955) C. R. Acad. Sci. Paris , vol.240 , pp. 1188-1189
    • Narayana, T.V.1
  • 162
    • 23344449378 scopus 로고
    • A note on the compositions of an integer
    • T.V. Narayana and G.E. Fulton. A note on the compositions of an integer. Canad. Math. Bull., 1:169–173, 1958.
    • (1958) Canad. Math. Bull. , vol.1 , pp. 169-173
    • Narayana, T.V.1    Fulton, G.E.2
  • 163
    • 0030527058 scopus 로고    scopus 로고
    • The enumeration of permutations with a prescribed number of “forbidden” patterns
    • J. Noonan and D. Zeilberger. The enumeration of permutations with a prescribed number of “forbidden” patterns. Adv. in Appl. Math., 17(4):381–407, 1996.
    • (1996) Adv. in Appl. Math. , vol.17 , Issue.4 , pp. 381-407
    • Noonan, J.1    Zeilberger, D.2
  • 164
    • 0000278117 scopus 로고
    • Asymptotic enumeration methods
    • Elsevier, Amsterdam
    • A.M. Odlyzko. Asymptotic enumeration methods. In Handbook of combinatorics, Vol. 1, 2, pages 1063–1229. Elsevier, Amsterdam, 1995.
    • (1995) Handbook of Combinatorics , vol.1 , Issue.2 , pp. 1063-1229
    • Odlyzko, A.M.1
  • 165
    • 0001237445 scopus 로고    scopus 로고
    • Combinatorics of geometrically distributed random variables: Left-to-right maxima
    • H. Prodinger. Combinatorics of geometrically distributed random variables: left-to-right maxima. Discrete Math., 153:253–270, 1996.
    • (1996) Discrete Math , vol.153 , pp. 253-270
    • Prodinger, H.1
  • 166
    • 67349130482 scopus 로고    scopus 로고
    • Records in geometrically distributed words: Sum of positions
    • H. Prodinger. Records in geometrically distributed words: sum of positions. Appl. Anal. Discrete Math., 2(2):234–240, 2008.
    • (2008) Appl. Anal. Discrete Math. , vol.2 , Issue.2 , pp. 234-240
    • Prodinger, H.1
  • 167
    • 0041440333 scopus 로고    scopus 로고
    • Enumeration of matchings: Problems and progress
    • L. J. Billera, A. Björner, C. Greene, R. E. Simion, and R. P. Stanley, editors, Cambridge University Press
    • J. Propp. Enumeration of matchings: problems and progress. In L. J. Billera, A. Björner, C. Greene, R. E. Simion, and R. P. Stanley, editors, New perspectives in algebraic combinatorics, volume38ofMathematical Sciences Research Institute Publications, pages 255–291. Cambridge University Press, 1999.
    • (1999) New Perspectives in Algebraic Combinatorics, Volume38ofmathematical Sciences Research Institute Publications , pp. 255-291
    • Propp, J.1
  • 168
    • 0345754980 scopus 로고    scopus 로고
    • Restricted words by adjacencies
    • D. Rawlings. Restricted words by adjacencies. Discrete Math., 220:183– 200, 2000.
    • (2000) Discrete Math , vol.220 , pp. 183-200
    • Rawlings, D.1
  • 169
    • 3042557039 scopus 로고    scopus 로고
    • Asymptotics of the number of k-words with an l-descent
    • A. Regev. Asymptotics of the number of k-words with an l-descent. Electron.J.Combin., 5:#R15, 1998.
    • (1998) Electron.J.Combin. , vol.5 , pp. R15
    • Regev, A.1
  • 171
  • 172
    • 0037339422 scopus 로고    scopus 로고
    • QMultiSum—a package for proving q-hypergeometric multiple summation identities
    • A. Riese. qMultiSum—a package for proving q-hypergeometric multiple summation identities. J. Symbolic Comput., 35(3):349–376, 2003.
    • (2003) J. Symbolic Comput. , vol.35 , Issue.3 , pp. 349-376
    • Riese, A.1
  • 175
    • 47949107323 scopus 로고    scopus 로고
    • Proper partitions of a polygon and k-Catalan numbers
    • B.E. Sagan. Proper partitions of a polygon and k-Catalan numbers. Ars Combin., 88:109–124, 2008.
    • (2008) Ars Combin , vol.88 , pp. 109-124
    • Sagan, B.E.1
  • 176
    • 31544480368 scopus 로고    scopus 로고
    • Pattern avoidance in compositions and multiset permutations
    • C.D. Savage and H.S. Wilf. Pattern avoidance in compositions and multiset permutations. Adv. in Appl. Math., 36(2):194–201, 2006.
    • (2006) Adv. in Appl. Math. , vol.36 , Issue.2 , pp. 194-201
    • Savage, C.D.1    Wilf, H.S.2
  • 177
    • 0001259916 scopus 로고
    • Longest increasing and decreasing subsequences
    • C. Schensted. Longest increasing and decreasing subsequences. Canad. J. Math., 13:179–191, 1961.
    • (1961) Canad. J. Math. , vol.13 , pp. 179-191
    • Schensted, C.1
  • 178
    • 0039090723 scopus 로고
    • A bijective proof on circular compositions
    • R. Servedio and Y.-N. Yeh. A bijective proof on circular compositions. Bull. Inst. Math. Acad. Sinica, 23(4):283–293, 1995.
    • (1995) Bull. Inst. Math. Acad. Sinica , vol.23 , Issue.4 , pp. 283-293
    • Servedio, R.1    Yeh, Y.-N.2
  • 184
    • 80053793949 scopus 로고    scopus 로고
    • Über unendliche Zahlenreihen
    • Trygve Nagell, Atle Selberg, Sigmund Selberg, and Knut Thalberg, editors, Universitetsforlaget, 1977. Originally published in Kra. Vidensk. Selsl. Skrifter. I. Mat. Nat. Kl. 1906. No. 7. Kra. 1906
    • Axel Thue. Über unendliche Zahlenreihen. In Trygve Nagell, Atle Selberg, Sigmund Selberg, and Knut Thalberg, editors, Selected Mathematical papers of Axel Thue, pages 139–158. Universitetsforlaget, 1977. Originally published in Kra. Vidensk. Selsl. Skrifter. I. Mat. Nat. Kl. 1906. No. 7. Kra. 1906.
    • Selected Mathematical Papers of Axel Thue , pp. 139-158
    • Thue, A.1
  • 185
    • 0002647237 scopus 로고    scopus 로고
    • Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen
    • Trygve Nagell, Atle Selberg, Sigmund Selberg, and Knut Thalberg, editors, Universitetsforlaget, 1977. Originally published in Kra. Vidensk. Selsl. Skrifter. I. Mat. Nat. Kl. 1912. No. 1. Kra. 1912
    • Axel Thue. Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. In Trygve Nagell, Atle Selberg, Sigmund Selberg, and Knut Thalberg, editors, Selected Mathematical papers of Axel Thue, pages 413–478. Universitetsforlaget, 1977. Originally published in Kra. Vidensk. Selsl. Skrifter. I. Mat. Nat. Kl. 1912. No. 1. Kra. 1912.
    • Selected Mathematical Papers of Axel Thue , pp. 413-478
    • Thue, A.1
  • 186
    • 0004996591 scopus 로고    scopus 로고
    • Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln
    • Trygve Nagell, Atle Selberg, Sigmund Selberg, and Knut Thalberg, editors, Universitetsforlaget, 1977. Originally published in Kra. Vidensk. Selsl. Skrifter. I. Mat. Nat. Kl. 1914. No. 10. Kra. 1914
    • Axel Thue. Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln. In Trygve Nagell, Atle Selberg, Sigmund Selberg, and Knut Thalberg, editors, Selected Mathematical papers of Axel Thue, pages 493–524. Universitetsforlaget, 1977. Originally published in Kra. Vidensk. Selsl. Skrifter. I. Mat. Nat. Kl. 1914. No. 10. Kra. 1914.
    • Selected Mathematical Papers of Axel Thue , pp. 493-524
    • Thue, A.1
  • 187
    • 0035634442 scopus 로고    scopus 로고
    • On the distributions of the lengths of the longest monotone subsequences in random words
    • C.A. Tracy and H. Widom. On the distributions of the lengths of the longest monotone subsequences in random words. Probab. Theory Related Fields, 119(3):350–380, 2001.
    • (2001) Probab. Theory Related Fields , vol.119 , Issue.3 , pp. 350-380
    • Tracy, C.A.1    Widom, H.2
  • 188
    • 21844508584 scopus 로고
    • The ranking problem of a Gray code for compositions
    • A.J. van Zanten. The ranking problem of a Gray code for compositions. Ars Combin., 41:257–268, 1995.
    • (1995) Ars Combin , vol.41 , pp. 257-268
    • van Zanten, A.J.1
  • 189
    • 0009366897 scopus 로고
    • Academic Press, New York-London
    • N.Y. Vilenkin. Combinatorics. Academic Press, New York-London, 1971.
    • (1971) Combinatorics
    • Vilenkin, N.Y.1
  • 190
    • 0011537555 scopus 로고
    • P, q-Stirling numbers and set partition statistics
    • M. Wachs and D. White. p, q-Stirling numbers and set partition statistics. J. Combin. Theory Ser. A, 56(1):27–46, 1991.
    • (1991) J. Combin. Theory Ser. A , vol.56 , Issue.1 , pp. 27-46
    • Wachs, M.1    White, D.2
  • 194
    • 0022133877 scopus 로고
    • Resurrecting the asymptotics of linear recurrences
    • J. Wimp and D. Zeilberger. Resurrecting the asymptotics of linear recurrences. J. Math. Anal. Appl., 111(1):162–176, 1985.
    • (1985) J. Math. Anal. Appl. , vol.111 , Issue.1 , pp. 162-176
    • Wimp, J.1    Zeilberger, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.