Stirling numbers interpolation using permutations with forbidden subsequences

Discrete Mathematics

Volumn 246, Issue 1-3, 2002, Pages 177-195

  Labelle, G ^a   Leroux, P ^b   Pergola, E ^a   Pinzani, R ^b  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31244435703     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(01)00257-6     Document Type: Article

References (27)

1. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, ECO: A methodology for the enumeration of combinatorial objects, J. Difference Equations Appl. 5 (1999) 435-490.
2. E. Barcucci, A. Del Lungo, E. Pergola, Random generation of tree and other combinatorial objects, Theoret. Comput. Sci. 218 (1999) 219-232.
3. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, From Motzkin to Catalan permutations, Discrete Math. 217 (2000) 33-49.
4. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, Permutation avoiding an increasing number of length-increasing forbidden subsequences, Discrete Math. Theoret. Comput. Sci. 4 (2000) 31-44.
5. M. Bôna, Permutations avoiding certain patterns, The case of length 4 and some generalizations, Discrete Math. 175 (1997) 55-67.
6. M. Böna, Exact enumeration of 1342-avoiding permutations; a close link with labelled trees and planar maps, J. Combin. Theory Ser. A 80 (1997) 257-272.
7. M. Bôna, The solution of a conjecture of Stanley and Wilf for all layered patterns, Proceedings of the 11th FPSAC, Barcelone, 1999, pp. 62-71.
8. L.M. Butler, The q-\og concavity of ç-binomial coefficients, J. Combin. Theory Ser. A 54 (1990) 53-62.
9. F.R.K. Chung, R.L. Graham, V.E. Hoggatt, M. Kleiman, The number of Baxter permutations, J. Combin. Theory Ser. A 24 (1978) 382-394.
10. L. Comtet, Advanced Combinatorics, Reidel, Dordrecht, 1979.
11. A.M. Garsia, J.B. Remmel, q-Counting rook configurations and a formula of Frobenius, J. Combin. Theory Ser. A 41 (1986) 246-275.
12. I.M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990) 257-285.
13. HAV. Gould, The g-Stirling numbers of first and second kinds, Duke Math. J. 28 (1961) 281-289.
14. O. Guibert, Combinatoire des permutations àmotifs exclus en liaison avec les mots, les cartes planaires et les tableaux de Young, Thèse de l'Université Bordeaux 1, 1996.
15. P. Leroux, Reduced matrices and q-log concavity properties of q-Stirling numbers, J. Combin. Theory Ser. A 54 (1990) 64-84.
16. A. .De 'Médicis, P. Leroux, A unified combinatorial approach for q-(snd p,q-) Stirling numbers, Jr-Statist. Plann. Inference 34 (1993) 89-105.
17. A. De Médicis, P. Leroux, Generalized Stirling numbers, convolution formulae and p, q-analogues, Canad. J. Math. 47 (1995) 474-499.
18. S.C. Milne, A ç-analog of restricted growth functions, Dobinski's equality, and Charlier polynomials, Trans. Amer. Math. Soc. 245 (1978) 89-118.
19. S.C. Milne, Restricted growth functions, rank row matchings of partition lattices, and g-Stirling numbers, Adv. Math. 43 (1982) 173-196.
20. S.C. Milne, Mapping of subspaces into subsets, J. Combin. Theory Ser. A 33 (1982) 36-47.
21. A. Regev, Asymptotic values for degrees associated with strips of Young diagrams, Adv. Math. 41 (1981) 115-136.
22. J. Riordan, An Introduction to Combinatorial Analysis, Wiley, New York, 1958.
23. R. Simion, F.W. Schmidt, Restricted permutations, European J. Combin. 6 (1985) 383-406.
24. N. Sloane, S. Ploufîe, Encyclopedia of Integer Sequences, Academic Press, New York, 1995.
25. M. Wachs, D. White, p, q-Stirling numbers and set partition statistics, J. Combin. Theory Ser. A 56 (1991) 27-46.
26. J. West, Permutations with forbidden subsequences and stack-sortable permutations, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, 1990.
27. J. West, Generating trees and forbidden subsequences, Discrete Math. 157 (1996) 363-374.