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Volumn 102, Issue 1, 2003, Pages 63-87

Bell numbers, their relatives, and algebraic differential equations

Author keywords

Algebraic differential equation; Bell number; Continued fraction; Crossing; Ordinary generating function; Set partition

Indexed keywords


EID: 0038706493     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-3165(03)00014-1     Document Type: Article
Times cited : (48)

References (43)
  • 2
    • 0000970787 scopus 로고
    • On the Vassiliev knot invariants
    • D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423-472.
    • (1995) Topology , vol.34 , pp. 423-472
    • Bar-Natan, D.1
  • 5
    • 0038236844 scopus 로고
    • An asymptotic expansion for the coefficients of some power series. II. Lagrange inversion
    • E.A. Bender, L.B. Richmond, An asymptotic expansion for the coefficients of some power series. II. Lagrange inversion, Discrete Math. 50 (1984) 135-141.
    • (1984) Discrete Math. , vol.50 , pp. 135-141
    • Bender, E.A.1    Richmond, L.B.2
  • 6
    • 0009773435 scopus 로고    scopus 로고
    • Stirling numbers and Bell numbers: Their role in combinatorics and probability
    • D. Branson, Stirling numbers and Bell numbers: their role in combinatorics and probability, Math. Sci. 25 (2000) 1-31.
    • (2000) Math. Sci. , vol.25 , pp. 1-31
    • Branson, D.1
  • 7
    • 4243524736 scopus 로고    scopus 로고
    • On the problem of uniqueness for the maximum Stirling number(s) of the second kind
    • A01
    • E.R. Canfield, C. Pomerance, On the problem of uniqueness for the maximum Stirling number(s) of the second kind, Integers 2 (2002) A01, 13pp.
    • (2002) Integers , vol.2 , pp. 13
    • Canfield, E.R.1    Pomerance, C.2
  • 8
    • 0035642626 scopus 로고    scopus 로고
    • Generalized pattern avoidance
    • A. Claesson, Generalized pattern avoidance, European J. Combin. 22 (2001) 961-971.
    • (2001) European J. Combin. , vol.22 , pp. 961-971
    • Claesson, A.1
  • 9
    • 0004258018 scopus 로고
    • Advanced Combinatorics
    • D. Reidel Publication Company, Boston, MA
    • L. Comtet, Advanced Combinatorics, D. Reidel Publication Company, Boston, MA, 1974.
    • (1974)
    • Comtet, L.1
  • 10
    • 0038284458 scopus 로고    scopus 로고
    • Plane Algebraic Curves
    • Providence, RI
    • G. Fischer, Plane Algebraic Curves, Amer. Math. Sci., Providence, RI, 2001.
    • (2001) Amer. Math. Sci.
    • Fischer, G.1
  • 11
    • 0042309538 scopus 로고
    • Combinatorial aspects of continued fractions
    • P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980) 125-161.
    • (1980) Discrete Math. , vol.32 , pp. 125-161
    • Flajolet, P.1
  • 12
    • 0038284451 scopus 로고    scopus 로고
    • Analytic combinatorics of chord diagrams
    • D. Krob, A.A. Mikhalev, A.V. Mikhalev (Eds.), FPSAC'00, Moscow, Russia, June 26-30, 2000, Springer, Berlin
    • P. Flajolet, M. Noy, Analytic combinatorics of chord diagrams, in: D. Krob, A.A. Mikhalev, A.V. Mikhalev (Eds.), Formal Power Series and Algebraic Combinatorics, FPSAC'00, Moscow, Russia, June 26-30, 2000, Springer, Berlin, 2000, pp. 191-201.
    • (2000) Formal Power Series and Algebraic Combinatorics , pp. 191-201
    • Flajolet, P.1    Noy, M.2
  • 13
    • 85013672888 scopus 로고
    • Non-overlapping partitions, continued fractions, Bessel functions and a divergent series
    • P. Flajolet, R. Schott, Non-overlapping partitions, continued fractions, Bessel functions and a divergent series, European J. Combin. 11 (1990) 421-432.
    • (1990) European J. Combin. , vol.11 , pp. 421-432
    • Flajolet, P.1    Schott, R.2
  • 15
    • 0038575599 scopus 로고
    • New modular properties of Bell numbers
    • N. Kahale, New modular properties of Bell numbers, J. Combin. Theory Ser. A 58 (1991) 147-152.
    • (1991) J. Combin. Theory Ser. A , vol.58 , pp. 147-152
    • Kahale, N.1
  • 16
    • 0346172929 scopus 로고    scopus 로고
    • Counting pattern-free set partitions II: Noncrossing and other hypergraphs
    • R34
    • M. Klazar, Counting pattern-free set partitions II: noncrossing and other hypergraphs, Electron. J. Combin. 7 (2000) R34, 25pp.
    • (2000) Electron. J. Combin. , vol.7 , pp. 25
    • Klazar, M.1
  • 17
    • 85031190333 scopus 로고    scopus 로고
    • Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings
    • to appear
    • M. Klazar, Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings, Adv. Appl. Math., to appear.
    • Adv. Appl. Math.
    • Klazar, M.1
  • 19
    • 0037899420 scopus 로고
    • Multisectioned moments of Stirling numbers of the second kind
    • D.H. Lehmer, Multisectioned moments of Stirling numbers of the second kind, J. Combin. Theory Ser. A 15 (1973) 210-224.
    • (1973) J. Combin. Theory Ser. A , vol.15 , pp. 210-224
    • Lehmer, D.H.1
  • 20
    • 0036445108 scopus 로고    scopus 로고
    • Free cumulants and enumeration of connected partitions
    • F. Lehner, Free cumulants and enumeration of connected partitions, European J. Combin. 23 (2002) 1025-1031.
    • (2002) European J. Combin. , vol.23 , pp. 1025-1031
    • Lehner, F.1
  • 21
    • 0038236843 scopus 로고
    • A gap theorem for power series solutions of algebraic differential equations
    • L. Lipshitz, L.A. Rubel, A gap theorem for power series solutions of algebraic differential equations, Amer. J. Math. 108 (1986) 1193-1214.
    • (1986) Amer. J. Math. , vol.108 , pp. 1193-1214
    • Lipshitz, L.1    Rubel, L.A.2
  • 22
    • 0003686156 scopus 로고
    • Combinatorial Problems and Exercises
    • Akadémiai Kiadó, Budapest
    • L. Lovász, Combinatorial Problems and Exercises, Akadémiai Kiadó, Budapest, 1993.
    • (1993)
    • Lovász, L.1
  • 23
    • 0009177885 scopus 로고
    • Über Dirichletsche Reihen und algebraische Differentialgleichungen
    • A. Ostrowski, Über Dirichletsche Reihen und algebraische Differentialgleichungen, Math. Z. 8 (1920) 241-298.
    • (1920) Math. Z. , vol.8 , pp. 241-298
    • Ostrowski, A.1
  • 24
    • 0031532214 scopus 로고    scopus 로고
    • Some probabilistic aspects of set partitions
    • J. Pitman, Some probabilistic aspects of set partitions, Amer. Math. Monthly 104 (1997) 201-209.
    • (1997) Amer. Math. Monthly , vol.104 , pp. 201-209
    • Pitman, J.1
  • 25
    • 0038236841 scopus 로고
    • On the number of Fibonacci partitions of a set
    • H. Prodinger, On the number of Fibonacci partitions of a set, Fibonacci Quart. 19 (1981) 463-465.
    • (1981) Fibonacci Quart. , vol.19 , pp. 463-465
    • Prodinger, H.1
  • 26
    • 0037561354 scopus 로고
    • Ordered Fibonacci partitions
    • H. Prodinger, Ordered Fibonacci partitions, Canad. Math. Bull. 26 (1983) 312-316.
    • (1983) Canad. Math. Bull. , vol.26 , pp. 312-316
    • Prodinger, H.1
  • 27
    • 0013559753 scopus 로고
    • Some research problems about algebraic differential equations
    • L.A. Rubel, Some research problems about algebraic differential equations, Trans. Amer. Math. Soc. 280 (1983) 43-52.
    • (1983) Trans. Amer. Math. Soc. , vol.280 , pp. 43-52
    • Rubel, L.A.1
  • 28
    • 84972583740 scopus 로고
    • Some research problems about algebraic differential equations II
    • L.A. Rubel, Some research problems about algebraic differential equations II, Illinois J. Math. 36 (1992) 659-680.
    • (1992) Illinois J. Math. , vol.36 , pp. 659-680
    • Rubel, L.A.1
  • 29
    • 0003870963 scopus 로고
    • The Basic Theory of Power Series
    • Friedr. Viewegh & Sohn, Braunschweig/Wiesbaden
    • J.M. Ruiz, The Basic Theory of Power Series, Friedr. Viewegh & Sohn, Braunschweig/Wiesbaden, 1993.
    • (1993)
    • Ruiz, J.M.1
  • 30
    • 84978694646 scopus 로고
    • On the distribution of values of recurring sequences and the Bell numbers in finite fields
    • I.E. Shparlinskiy, On the distribution of values of recurring sequences and the Bell numbers in finite fields, European J. Combin. 12 (1991) 81-87.
    • (1991) European J. Combin. , vol.12 , pp. 81-87
    • Shparlinskiy, I.E.1
  • 31
    • 0000790354 scopus 로고    scopus 로고
    • Noncrossing partitions
    • R. Simion, Noncrossing partitions, Discrete Math. 217 (2000) 367-409.
    • (2000) Discrete Math. , vol.217 , pp. 367-409
    • Simion, R.1
  • 32
    • 0003633725 scopus 로고    scopus 로고
    • The On-Line Encyclopedia of Integer Sequences
    • (Ed.), published electronically at
    • N.J.A. Sloane, (Ed.), The On-Line Encyclopedia of Integer Sequences, 2002, published electronically at http://www.research.att.com/~njas/sequences/
    • (2002)
    • Sloane, N.J.A.1
  • 33
    • 0000410641 scopus 로고
    • Differentiably finite power series
    • R.P. Stanley, Differentiably finite power series, European J. Combin. 1 (1980) 175-188.
    • (1980) European J. Combin. , vol.1 , pp. 175-188
    • Stanley, R.P.1
  • 34
    • 0003652674 scopus 로고    scopus 로고
    • Wadsworth & Brooks/Cole, Monterey, CA
    • R.P. Stanley, Enumerative Combinatorics, Vol. I, Wadsworth & Brooks/Cole, Monterey, CA, 1986.
    • (1986) Enumerative Combinatorics , vol.1
    • Stanley, R.P.1
  • 35
    • 0003652674 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R.P. Stanley, Enumerative Combinatorics, Vol. II, Cambridge University Press, Cambridge, UK, 1999.
    • (1999) Enumerative Combinatorics , vol.2
    • Stanley, R.P.1
  • 36
    • 0038284449 scopus 로고
    • On a class of linked diagrams, I. Enumeration
    • P.R. Stein, On a class of linked diagrams, I. Enumeration, J. Combin. Theory Ser. A 24 (1978) 357-366.
    • (1978) J. Combin. Theory Ser. A , vol.24 , pp. 357-366
    • Stein, P.R.1
  • 37
    • 0011508783 scopus 로고    scopus 로고
    • On the number of chord diagrams
    • A. Stoimenow, On the number of chord diagrams, Discrete Math. 218 (2000) 209-233.
    • (2000) Discrete Math. , vol.218 , pp. 209-233
    • Stoimenow, A.1
  • 38
    • 0038575600 scopus 로고    scopus 로고
    • Some remarks on a product expansion: An unexplored partition function
    • F.G. Garvan, M.E.H. Ismail (Eds.), (Gainesville, FL, 1999), Kluwer, Dordrecht
    • M.V. Subbarao, A. Verma, Some remarks on a product expansion: an unexplored partition function, in: F.G. Garvan, M.E.H. Ismail (Eds.), Symbolic Computations, Number Theory, Special Functions, Physics and Combinatorics (Gainesville, FL, 1999), Kluwer, Dordrecht, 2001, pp. 267-283.
    • (2001) Symbolic Computations, Number Theory, Special Functions, Physics and Combinatorics , pp. 267-283
    • Subbarao, M.V.1    Verma, A.2
  • 40
    • 0004055955 scopus 로고
    • Algebraic Curves
    • Princeton University Press, Princeton, NJ
    • R.J. Walker, Algebraic Curves, Princeton University Press, Princeton, NJ, 1950.
    • (1950)
    • Walker, R.J.1
  • 41
    • 0022133877 scopus 로고
    • Resurrecting the asymptotics of linear recurrences
    • J. Wimp, D. Zeilberger, Resurrecting the asymptotics of linear recurrences, J. Math. Anal. Appl. 111 (1985) 162-176.
    • (1985) J. Math. Anal. Appl. , vol.111 , pp. 162-176
    • Wimp, J.1    Zeilberger, D.2
  • 42
    • 0037561350 scopus 로고    scopus 로고
    • Bell numbers and k-trees
    • W. Yang, Bell numbers and k-trees, Discrete Math. 156 (1996) 247-252.
    • (1996) Discrete Math. , vol.156 , pp. 247-252
    • Yang, W.1
  • 43
    • 0037561341 scopus 로고    scopus 로고
    • On a multiplicative partition function
    • R19
    • Y. Yang, On a multiplicative partition function, Electron. J. Combin. 8 (2001) R19, 14pp.
    • (2001) Electron. J. Combin. , vol.8 , pp. 14
    • Yang, Y.1


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