Enumeration of permutations containing a prescribed number of occurences of a pattern of length three

Advances in Applied Mathematics

Volumn 30, Issue 4, 2003, Pages 607-632

  Fulmek, Markus ^a  

^a UNIVERSITY OF VIENNA   (Austria)

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[No Author keywords available]

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EID: 0037505582     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-8858(02)00501-8     Document Type: Article

References (23)

1. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, Permutations with one forbidden subsequence of increasing length, in: Proc. of the 9th FPSAC, Vienna, 1997, pp. 49-60.
2. n to n!: Permutations avoiding sj(j + 1)(j + 2), in: Proc. of the 10th FPSAC, Toronto, 1998, pp. 31-41.
3. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, Permutations avoiding an increasing number of length-increasing forbidden subsequences, Discrete Math. Theoret. Comput. Sci. 4 (2000) 31-44.
4. M. Bóna, Exact enumeration of 1342-avoiding permutation: A close link with labelled trees and planar maps, J. Combin. Theory Ser. A 80 (1997) 257-272.
5. M. Bóna, The number of permutations with exactly r 132-subsequences is P-recursive in the size!, Adv. in Appl. Math. 18 (1997) 510-522.
6. M. Bóna, Permutations avoiding certain patterns: The case of length 4 and some generalizations, Discrete Math. 175 (1997) 55-67.
7. M. Bóna, Permutations with one or two 132-subsequences, Discrete Math. 181 (1998) 267-274.
8. E.S. Egge, Restricted permutations related to Fibonacci numbers and k-generalized Fibonacci numbers, Preprint, math.CO/0109219v1, 2001.
9. C. Krattenthaler, Permutations with restricted patterns and Dyck paths, Adv. in Appl. Math. 27 (2001) 510-530.
10. T. Mansour, Private communication, 2001.
11. T. Mansour, A. Vainshtein, Counting occurrences of 132 in a permutation, Preprint, math.CO/0107073v2, Adv. in Appl. Math., in print.
12. T. Mansour, A. Vainshtein, Layered restrictions and Chebyshev polynomials, Ann. Combin., in print.
13. T. Mansour, A. Vainshtein, Restricted permutations, continued fractions and Chebyshev polynomials, Electron. J. Combin. 7 (2000) R17.
14. T. Mansour, A. Vainshtein, Restricted (132)-avoiding permutations, Adv. in Appl. Math. 26 (2001) 258-269.
15. T. Mansour, A. Vainshtein, Restricted permutations and Chebyshev polynomials, Sém. Lothar. Combin. 47 (2001) 17.
16. J. Noonan, The number of permutations containing exactly one increasing subsequence of length 3, Discrete Math. 152 (1996) 307-313.
17. J. Noonan, D. Zeilberger, The enumeration of permutations with a prescribed number of "forbidden" patterns, Adv. in Appl. Math. 17 (1996) 381-404.
18. A. Robertson, Permutations restricted by two distinct patterns of length three, Adv. in Appl. Math. 27 (2001) 548-561.
19. A. Robertson, H. Wilf, D. Zeilberger, Permutation patterns and continued fractions, Electron. J. Combin. 6 (1999) R38.
20. R. Simion, F.W. Schmidt, Restricted permutations, European J. Combin. 6 (1985) 383-406.
21. R.P. Stanley, Enumerative Combinatorics 1, Wadsworth, Monterey, CA, 1986.
22. R.P. Stanley, Enumerative Combinatorics 2, in: Cambridge Stud. Adv. Math., Vol. 62, Cambridge Univ. Press, Cambridge, 1999.
23. J. West, Permutations with forbidden subsequences; and, stack sortable permutations, PhD thesis, Massachusetts Institute of Technology, 1990.