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Volumn 339, Issue 1, 2005, Pages 7-18

Pattern avoidance: Themes and variations

Author keywords

Combinatorics on words; Words avoiding patterns

Indexed keywords

ALGEBRA; INTEGER PROGRAMMING; MATHEMATICAL MODELS; THEOREM PROVING;

EID: 18644366449     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.01.004     Document Type: Conference Paper
Times cited : (59)

References (70)
  • 7
    • 33845218374 scopus 로고
    • Avoidable patterns in strings of symbols
    • D.R. Bean, A. Ehrenfeucht, and G. McNulty Avoidable patterns in strings of symbols Pacific J. Math. 85 1979 261 294; MR 81i:20075.
    • (1979) Pacific J. Math. , vol.85 , pp. 261-294
    • Bean, D.R.1    Ehrenfeucht, A.2    McNulty, G.3
  • 8
    • 0242368982 scopus 로고
    • An application of Lovász local lemma: There exists an infinite 01-sequence containing no near identical intervals
    • Eger
    • J. Beck, An application of Lovász local lemma: there exists an infinite 01-sequence containing no near identical intervals, Finite and Infinite Sets, Vols. I, II, Eger, 1981
    • (1981) Finite and Infinite Sets , vol.1-2
    • Beck, J.1
  • 11
    • 38249032793 scopus 로고
    • Uniformly growing k-th powerfree homomorphisms
    • F.J. Brandenburg Uniformly growing k-th powerfree homomorphisms Theoret. Comput. Sci. 23 1983 69 82
    • (1983) Theoret. Comput. Sci. , vol.23 , pp. 69-82
    • Brandenburg, F.J.1
  • 12
    • 0007132916 scopus 로고
    • Non-repetitive sequences on three symbols
    • J. Brinkhuis Non-repetitive sequences on three symbols Quart. J. Math. Oxford Ser. 34 2 1983 145 149
    • (1983) Quart. J. Math. Oxford Ser. , vol.34 , Issue.2 , pp. 145-149
    • Brinkhuis, J.1
  • 13
    • 0023965026 scopus 로고
    • Multidimensional unrepetitive configurations
    • A. Carpi Multidimensional unrepetitive configurations Theoret. Comput. Sci. 56 2 1988 233 241
    • (1988) Theoret. Comput. Sci. , vol.56 , Issue.2 , pp. 233-241
    • Carpi, A.1
  • 14
    • 0027624812 scopus 로고
    • Overlap-free words and finite automata
    • A. Carpi Overlap-free words and finite automata Theoret. Comput. Sci. 115 2 1993 243 260
    • (1993) Theoret. Comput. Sci. , vol.115 , Issue.2 , pp. 243-260
    • Carpi, A.1
  • 15
    • 18644365042 scopus 로고
    • On representation systems
    • A. Carpi On representation systems Internat. J. Algebra Comput. 4 4 1994 657 690
    • (1994) Internat. J. Algebra Comput. , vol.4 , Issue.4 , pp. 657-690
    • Carpi, A.1
  • 16
    • 0041353863 scopus 로고    scopus 로고
    • On the number of Abelian square-free words on four letters
    • A. Carpi On the number of Abelian square-free words on four letters Discrete Appl. Math. 81 1998 155 167
    • (1998) Discrete Appl. Math. , vol.81 , pp. 155-167
    • Carpi, A.1
  • 17
    • 0039789462 scopus 로고    scopus 로고
    • On abelian squares and substitutions
    • A. Carpi On abelian squares and substitutions Theoret. Comput. Sci. 218 1 1999 61 81
    • (1999) Theoret. Comput. Sci. , vol.218 , Issue.1 , pp. 61-81
    • Carpi, A.1
  • 18
    • 0039789462 scopus 로고    scopus 로고
    • On Abelian squares and substitutions
    • A. Carpi On Abelian squares and substitutions Theoret. Comput. Sci. 218 1999 61 81
    • (1999) Theoret. Comput. Sci. , vol.218 , pp. 61-81
    • Carpi, A.1
  • 19
    • 0041756479 scopus 로고
    • Counting overlap-free binary words
    • Springer, Berlin
    • J. Cassaigne, Counting Overlap-free Binary Words, Lecture Notes in Computer Science, Vol. 665, Springer, Berlin, 1993, pp. 216-225.
    • (1993) Lecture Notes in Computer Science , vol.665 , pp. 216-225
    • Cassaigne, J.1
  • 21
    • 0041964331 scopus 로고
    • An algorithm to test if a given circular HD0L-language avoids a pattern
    • Hamburg
    • J. Cassaigne, An algorithm to test if a given circular HD0L-language avoids a pattern. Information Processing '94, Vol. I Hamburg, 1994
    • (1994) Information Processing '94 , vol.1
    • Cassaigne, J.1
  • 23
    • 0033263841 scopus 로고    scopus 로고
    • Words strongly avoiding fractional powers
    • J. Cassaigne, and J.D. Currie Words strongly avoiding fractional powers European J. Combin. 20 8 1999 725 737
    • (1999) European J. Combin. , vol.20 , Issue.8 , pp. 725-737
    • Cassaigne, J.1    Currie, J.D.2
  • 25
    • 0026142121 scopus 로고
    • On the number of partially abelian square-free words on a three-letter alphabet
    • R. Cori, M.R. Formisano, On the number of partially abelian square-free words on a three-letter alphabet, Theoret. Comput. Sci. 81 (1) (1991) (Part A) 147-153.
    • (1991) Theoret. Comput. Sci. , vol.81 , Issue.1 PART A , pp. 147-153
    • Cori, R.1    Formisano, M.R.2
  • 26
    • 0000813621 scopus 로고
    • Sharp characterizations of squarefree morphisms
    • M. Crochemore Sharp characterizations of squarefree morphisms Theoret. Comput. Sci. 18 2 1982 221 226
    • (1982) Theoret. Comput. Sci. , vol.18 , Issue.2 , pp. 221-226
    • Crochemore, M.1
  • 27
    • 0038693845 scopus 로고    scopus 로고
    • There are ternary circular square-free words of length n for n≥18
    • J.D. Currie, There are ternary circular square-free words of length n for n ≥ 18, Elec. J. Comb. 9(1) (2002) N10.
    • (2002) Elec. J. Comb. , vol.9 , Issue.1
    • Currie, J.D.1
  • 28
    • 33846217586 scopus 로고    scopus 로고
    • Circular words avoiding patterns
    • M. Ito, M. Toyama (Eds.) Kyoto, Japan, Lecture Notes in Computer Science, to appear, Springer, Berlin
    • J.D. Currie, D.S. Fitzpatrick, Circular words avoiding patterns, in: M. Ito, M. Toyama (Eds.), Developments in Language Theory, Sixth Internat. Conf., DLT 2002, Kyoto, Japan, Lecture Notes in Computer Science, to appear, Springer, Berlin, 2003.
    • (2003) Developments in Language Theory, Sixth Internat. Conf., DLT 2002
    • Currie, J.D.1    Fitzpatrick, D.S.2
  • 29
    • 0035602469 scopus 로고    scopus 로고
    • Avoiding patterns in the Abelian sense
    • J.D. Currie, and V. Linek Avoiding patterns in the Abelian sense Canadian J. Math. 51 4 2001 696 714
    • (2001) Canadian J. Math. , vol.51 , Issue.4 , pp. 696-714
    • Currie, J.D.1    Linek, V.2
  • 30
  • 31
  • 32
  • 33
    • 0039162445 scopus 로고
    • Strongly non-repetitive sequences and progression-free sets
    • F.M. Dekking Strongly non-repetitive sequences and progression-free sets J. Combin. Theory Ser. A 27 1979 181 185
    • (1979) J. Combin. Theory Ser. A , vol.27 , pp. 181-185
    • Dekking, F.M.1
  • 34
    • 0010004382 scopus 로고    scopus 로고
    • There are more than 2(n/17) n-letter ternary square-free words
    • S.B. Ekhad, and D. Zeilberger There are more than 2 (n / 17) n-letter ternary square-free words J. Integer Seq. 1 1998 98.1.9
    • (1998) J. Integer Seq. , vol.1 , pp. 9819
    • Ekhad, S.B.1    Zeilberger, D.2
  • 36
    • 0040975969 scopus 로고
    • Strongly asymmetric sequences generated by a finite number of symbols
    • A.A. Evdomikov Strongly asymmetric sequences generated by a finite number of symbols Dokl. Akad. Nauk. SSSR 179 1968 1268 1271
    • (1968) Dokl. Akad. Nauk. SSSR , vol.179 , pp. 1268-1271
    • Evdomikov, A.A.1
  • 37
    • 0039197125 scopus 로고
    • Soviet Math. Dokl. 9 (1968) 536-539.
    • (1968) Soviet Math. Dokl. , vol.9 , pp. 536-539
  • 39
    • 2942702448 scopus 로고    scopus 로고
    • Improved bounds on the number of ternary square-free words
    • U. Grimm Improved bounds on the number of ternary square-free words J. Integer Seq. 4 2001
    • (2001) J. Integer Seq. , vol.4
    • Grimm, U.1
  • 40
    • 4043054972 scopus 로고    scopus 로고
    • Thue-like sequences and rainbow arithmetic progressions
    • Research Paper 44
    • J. Grytczuk, Thue-like sequences and rainbow arithmetic progressions, Electron. J. Combin. 9 (1) (2002) Research Paper 44, 10 pp.
    • (2002) Electron. J. Combin. , vol.9 , Issue.1
    • Grytczuk, J.1
  • 41
    • 0142199980 scopus 로고    scopus 로고
    • Pattern avoiding colorings of Euclidean spaces
    • J. Grytczuk Pattern avoiding colorings of Euclidean spaces Ars Combin. 64 2002 109 116
    • (2002) Ars Combin. , vol.64 , pp. 109-116
    • Grytczuk, J.1
  • 42
    • 18644374687 scopus 로고
    • On irreductible languages and nonrational numbers
    • S. Istrail On irreductible languages and nonrational numbers Bull. Math. Soc. Sci. Math. R. S. Roumanie, Tome 2169, nr. 3-4 1977 301 308
    • (1977) Bull. Math. Soc. Sci. Math. R. S. Roumanie , vol.2169 , Issue.3-4 , pp. 301-308
    • Istrail, S.1
  • 43
    • 51249191674 scopus 로고
    • Intervals in the lattice of varieties
    • J. Jezek Intervals in the lattice of varieties Algebra Universalis 6 1976 147 158
    • (1976) Algebra Universalis , vol.6 , pp. 147-158
    • Jezek, J.1
  • 44
    • 0002073948 scopus 로고
    • Characterization of the repetitive commutative semigroups
    • J. Justin Characterization of the repetitive commutative semigroups J. Algebra 21 1972 87 90
    • (1972) J. Algebra , vol.21 , pp. 87-90
    • Justin, J.1
  • 45
    • 0000155707 scopus 로고
    • On cube-free ω-words generated by binary morphisms
    • J. Karhumäki On cube-free ω -words generated by binary morphisms Discrete Appl. Math. 5 3 1983 279 297
    • (1983) Discrete Appl. Math. , vol.5 , Issue.3 , pp. 279-297
    • Karhumäki, J.1
  • 46
    • 11144354707 scopus 로고    scopus 로고
    • Polynomial versus exponential growth in repetition-free binary words
    • J. Karhumaki, and J. Shallit Polynomial versus exponential growth in repetition-free binary words J. Combin. Theory Ser. A 105 2004 335 347
    • (2004) J. Combin. Theory Ser. A , vol.105 , pp. 335-347
    • Karhumaki, J.1    Shallit, J.2
  • 47
    • 85029809939 scopus 로고
    • Abelian squares are avoidable on 4 letters
    • Automata, Languages and Programming Springer, Berlin
    • V. Keränen, Abelian squares are avoidable on 4 letters, Automata, Languages and Programming: Lecture Notes in Computer Science, Vol. 623, Springer, Berlin, 1992, pp. 41-52.
    • (1992) Lecture Notes in Computer Science , vol.623 , pp. 41-52
    • Keränen, V.1
  • 48
    • 0041457495 scopus 로고
    • A linear-time algorithm to decide whether a binary word contains an overlap
    • A.J. Kfoury A linear-time algorithm to decide whether a binary word contains an overlap RAIRO Inform. Théor. Appl. 22 2 1988 135 145
    • (1988) RAIRO Inform. Théor. Appl. , vol.22 , Issue.2 , pp. 135-145
    • Kfoury, A.J.1
  • 50
    • 38249028908 scopus 로고
    • Enumeration of irreducible binary words
    • Y. Kobayashi Enumeration of irreducible binary words Discrete Appl. Math. 20 3 1988 221 232
    • (1988) Discrete Appl. Math. , vol.20 , Issue.3 , pp. 221-232
    • Kobayashi, Y.1
  • 51
    • 84947749257 scopus 로고    scopus 로고
    • Minimal letter frequency in nth power-free binary words
    • Mathematical Foundations of Computer Science, Bratislava, 1997 Springer, Berlin
    • R. Kolpakov, G. Kucherov, Minimal letter frequency in n th power-free binary words, Mathematical Foundations of Computer Science, Bratislava, 1997, Lecture Notes in Computer Science, Vol. 1295, Springer, Berlin, 1997, pp. 347-357.
    • (1997) Lecture Notes in Computer Science , vol.1295 , pp. 347-357
    • Kolpakov, R.1    Kucherov, G.2
  • 52
    • 0347653264 scopus 로고    scopus 로고
    • On repetition-free binary words of minimal density
    • R. Kolpakov, G. Kucherov, and Y. Tarannikov On repetition-free binary words of minimal density Theoret. Comput. Sci. 218 1 1999 161 175
    • (1999) Theoret. Comput. Sci. , vol.218 , Issue.1 , pp. 161-175
    • Kolpakov, R.1    Kucherov, G.2    Tarannikov, Y.3
  • 53
    • 0014265483 scopus 로고
    • Mathematical model for cellular interaction in development. Parts I and II
    • A. Lindenmeyer Mathematical model for cellular interaction in development. Parts I and II J. Theoret. Biol. 18 1968 280 315
    • (1968) J. Theoret. Biol. , vol.18 , pp. 280-315
    • Lindenmeyer, A.1
  • 54
    • 18644370913 scopus 로고    scopus 로고
    • New problems of pattern avoidance
    • Aachen, World Sci. Publishing, River Edge, NJ
    • J. Loftus, J. Shallit, M.-W. Wang, New problems of pattern avoidance, Developments In Language Theory 1999, Aachen, World Sci. Publishing, River Edge, NJ, 2000, pp. 185-199.
    • (2000) Developments in Language Theory 1999 , pp. 185-199
    • Loftus, J.1    Shallit, J.2    Wang, M.-W.3
  • 55
    • 0024619876 scopus 로고
    • Some combinatorial properties of the Thue-Morse sequence and a problem of semigroups
    • A. Luca, and S. Varriccio Some combinatorial properties of the Thue-Morse sequence and a problem of semigroups Theoret. Comput. Sci. 63 1989 333 348
    • (1989) Theoret. Comput. Sci. , vol.63 , pp. 333-348
    • Luca, A.1    Varriccio, S.2
  • 56
  • 57
    • 84914087454 scopus 로고
    • Recurrent geodesics on a surface of negative curvature
    • M. Morse Recurrent geodesics on a surface of negative curvature Trans. Amer. Math. Soc. 22 1921 84 100
    • (1921) Trans. Amer. Math. Soc. , vol.22 , pp. 84-100
    • Morse, M.1
  • 58
    • 0042970957 scopus 로고    scopus 로고
    • The Goulden-Jackson cluster method: Extensions, applications, and implementations
    • J. Noonan, and D. Zeilberger The Goulden-Jackson cluster method extensions, applications, and implementations J. Difference Eq. Appl. 5 1999 355 377
    • (1999) J. Difference Eq. Appl. , vol.5 , pp. 355-377
    • Noonan, J.1    Zeilberger, D.2
  • 59
    • 0026839463 scopus 로고
    • Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10, and 11 letters
    • J.M. Ollagnier Proof of Dejean's conjecture for alphabets with 5, 6, 7, 8, 9, 10, and 11 letters Theoret. Comput. Sci. 95 1992 187 205
    • (1992) Theoret. Comput. Sci. , vol.95 , pp. 187-205
    • Ollagnier, J.M.1
  • 60
    • 0039348673 scopus 로고
    • A propos d'une conjecture de F. Dejean sur les répétitions dans les mots
    • J.-J. Pansiot A propos d'une conjecture de F. Dejean sur les répétitions dans les mots Discrete Appl. Math. 7 1984 297 311
    • (1984) Discrete Appl. Math. , vol.7 , pp. 297-311
    • Pansiot, J.-J.1
  • 62
    • 0009961377 scopus 로고
    • On the structure and extendibility of square-free words
    • Academic Press, New York
    • R.O. Shelton, On the structure and extendibility of square-free words, Combinatorics on Words: Progress and Perspectives, Academic Press, New York, 1983, pp. 101-188.
    • (1983) Combinatorics on Words: Progress and Perspectives , pp. 101-188
    • Shelton, R.O.1
  • 63
    • 0038072521 scopus 로고
    • Aperiodic words on three symbols I, II, III
    • 327 MR 82m:05004a-c
    • R.O. Shelton (I, II, III), R.P. Soni (II, III), Aperiodic words on three symbols I, II, III, J. Reine Agnew. Math. 321, 327, 330 (1981) 195-209,1-11,44-52; MR 82m:05004a-c.
    • (1981) J. Reine Agnew. Math. , vol.321-330 , pp. 195-209
    • Shelton, R.O.1    Soni, R.P.2
  • 64
    • 1942530645 scopus 로고    scopus 로고
    • The minimal density of a letter in an infinite ternary square-free word is 0.2746...
    • Article 02.2.2
    • Y. Tarannikov, The minimal density of a letter in an infinite ternary square-free word is 0.2746 ⋯, J. Integer Seq. 5 (2) (2002) Article 02.2.2.
    • (2002) J. Integer Seq. , vol.5 , Issue.2
    • Tarannikov, Y.1
  • 67
    • 0039754995 scopus 로고
    • Arithmetic progressions in partially ordered sets
    • W.T. Trotter, and P. Winkler Arithmetic progressions in partially ordered sets ORDER 4 1987 37 42
    • (1987) ORDER , vol.4 , pp. 37-42
    • Trotter, W.T.1    Winkler, P.2
  • 69
    • 0040820364 scopus 로고
    • Blocking sets of terms
    • A. Zimin Blocking sets of terms Mat. Sb. N.S. 119 161 1982
    • (1982) Mat. Sb. N.S. , vol.119 , Issue.161
    • Zimin, A.1
  • 70
    • 0038575544 scopus 로고
    • Blocking sets of terms
    • A. Zimin Blocking sets of terms Math. USSR Sb. 47 1984 353 364
    • (1984) Math. USSR Sb. , vol.47 , pp. 353-364
    • Zimin, A.1


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