Counting Pattern-free Set Partitions I: A Generalization of Stirling Numbers of the Second Kind

European Journal of Combinatorics

Volumn 21, Issue 3, 2000, Pages 367-378

  Klazar, Martin ^a,b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034382441     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.1999.0353     Document Type: Article

References (31)

1. N. Alon and E. Friedgut, On the number of permutations avoiding a given pattern, J. Comb. Theory, Ser. A, to appear.
2. H. W. Becker, Planar rhyme schemes, Bull. Am. Math. Soc., 58 (1952), 39.
3. M. Bóna, Exact enumeration of 1342-avoiding permutations: a close link with labeled trees and planar maps, J. Comb. Theory, Ser. A, 80 (1997), 257-272.
4. M. Bóna, Permutations avoiding certain patterns: the case of length 4 and some generalizations, Discrete Math., 175 (1997), 55-67.
5. M. Bóna, The solution of a conjecture of Stanley and Wilf for all layered patterns, J. Comb. Theory, Ser. A, 85 (1999), 96-104.
6. M. Bóna, Partitions with k crossings, Ramanujan J., 3 (1999), 215-220.
7. N. Dershowitz and S. Zaks, Ordered trees and non-crossing partitions, Discrete Math., 62 (1986), 215-218.
8. H. Edelsbrunner and M. Sharir, The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n - 2, Discrete Comput. Geom., 5 (1990), 35-42.
9. I. M. Gessel, Symmetric functions and P-recursiveness, J. Comb. Theory, Ser. A, 53 (1990), 257-285.
10. M. Katchalski and H. Last, On geometric graphs with no two edges in convex position, Discrete Comput. Geom., 19 (1998), 399-404.
11. M. Klazar, On abab-free and abba-free set partitions, Europ. J. Combinatorics, 17 (1996), 53-68.
12. M. Klazar, On the maximum lengths of Davenport-Schinzel sequences, in: Contemporary Trends in Discrete Mathematics, R. L. Graham, J. Kratochvíl, J. Nešetřil and F. S. Roberts (eds), American Mathematical Society, Providence, RI, 1999, pp. 169-178.
13. D. E. Knuth, The Art of Computer Programming, volume 3, Addison Wesley, Reading, MA, 1973.
14. G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Math., 1 (1972), 333-350.
15. J. B. Kruskal, The theory of well-quasi-ordering: a frequently discovered concept, J. Comb. Theory, Series A, 13 (1972), 297-305.
16. R. Laver, Well-quasi-orderings and sets of finite sequences, Math. Proc. Camb. Phil. Soc., 79 (1976), 1-10.
17. Y. Poupard, Étude et denombrement paralleles des partitions non croisées d'un cycle et des decoupage d'un polygone convexe, Discrete Math., 2 (1972), 279-288.
18. H. Prodinger, A correspondence between ordered trees and noncrossing partitions, Discrete Math., 46 (1983), 205-206.
19. A. Regev, Asymptotic values for degrees associated with strips of Young diagrams, Adv. Math., 41 (1981), 115-136.
20. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and their Geometric Applications, Cambridge University Press, Cambridge, UK, 1995.
21. R. Simion, Combinatorial statistics on non-crossing partitions, J. Comb. Theory, Ser. A, 66 (1994), 270-301.
22. R. Simion and F. W. Schmidt, Restricted permutations, Europ. J. Combinatorics, 6 (1985), 383-406.
23. R. Simion and D. Ullman, On the structure of the lattice of noncrossing partitions, Discrete Math., 98 (1991), 193-206.
24. R. Speicher, Free probability theory and non-crossing partitions, Semin. Lothar. Comb., 39 (1997), B39c, 38 pp.
25. Z. Stankova, Classification of forbidden subsequences of length 4, Europ. J. Combinatorics, 17 (1996), 501-517.
26. R. P. Stanley, Differentably finite power series, Europ. J. Combinatorics, 1 (1980), 175-188.
27. R. P. Stanley, Enumerative Combinatorics, volume 1, 2nd edn, Cambridge University Press, Cambridge, UK, 1997.
28. P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discrete Math., 26 (1979), 261-272.
29. M. S. Waterman, Applications of combinatorics to molecular biology, in: Handbook of Combinatorics, R. L. Graham, M. Grötschel and L. Lovász (eds), North-Holland, Amsterdam, 1995, pp. 1983-2001.
30. J. West, Generating trees and forbidden subsequences, Discrete Math., 157 (1996), 363-374.
31. A. Wiernik and M. Sharir, Planar realization of nonlinear Davenport-Schinzel sequences by segments, Discrete Comput. Geom., 3 (1988), 15-47.