Directed animals, forests and permutations

Discrete Mathematics

Volumn 204, Issue 1-3, 1999, Pages 41-71

  Barcucci, Elena ^a   Del Lungo, Alberto ^a   Pergola, Elisa ^a   Pinzani, Renzo ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Directed animals; Enumerative combinatorics; Permutations; Trees

Indexed keywords

EID: 0042707117     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(98)00366-5     Document Type: Article

References (20)

1. E. Barcucci, A. Del Lungo, S. Fezzi, R. Pinzani, Non-decreasing Dyck paths and q-Fibonacci numbers, Discrete. Math. 170 (1997) 211-217.
2. E. Barcucci, A. Del Lungo, S. Lanini, M. Macri, R. Pinzani, The inversion number of some permutations with forbidden subsequences, Proc. SOCA'96, Tianjin, 1996, pp. 21-32.
3. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, Towards a methodology for plane tree enumeration, in: B. Leclerc, J.Y. Thibon (Eds.), Proc. 7th FPSAC, Université deMarne-la-Vallée, 1995, pp. 53-65.
4. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, A methodology for plane tree enumeration, Discrete Math. 180 (1998) 45-64.
5. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, A construction for enumerating k-coloured Motzkin paths, Lecture Notes in Computers Science, 1st Annual Computing and Combinatorics Conf. (COCOON'95), Xi'an, China, 1995, pp. 254-263.
6. E. Barcucci, A. Del Lungo, E. Pergola, Permutations with one forbidden subsequence of increasing length, Proc. of 9th FPSAC, Vienna, 1997, pp. 49-60.
7. M. Bousquet-Mélou, New enumerative results on two-dimensional directed animals, in: B. Leclerc, J.Y. Thibon (Eds.), Proc. 7th FPSAC, Université de Marne-la-Vallée, Paris, 1995, pp. 103-116.
8. 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.
9. A.R. Conway, R. Brak, A.J. Guttmann, Directed animals on two-dimensional lattices, J. Phys. A 26 (1993) 3085-3091.
10. A.R. Conway, On the behaviour of self avoiding walks and related problems, Ph. D. Thesis, University of Melbourne, Australia, 1993.
11. B. Derrida, J.P. Nadal, J. Vannimenus, Directed lattice animals in 2 dimensions: numerical and exact results, J. Phys. A 43 (1982) 1561.
12. D. Dhar, M. Phani, M. Barma, Enumeration of directed site animals on two-dimensional lattices, J. Phys. A 15 (1982) L279-L284.
13. D. Gouyou-Beauchamps, X.G. Viennot, Equivalence of the two-dimensional directed animal problem to a one-dimensional path problem, Adv. Appl. Math. 9 (1988) 334-357.
14. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, New York, 1989.
15. O. Guibert, Combinatoires des permutations a motifs exclus en liaison avec mots, cartes planaires et tableaux de Young, Thèse no. 1416, Université Bordeaux I, decembre 1995.
16. D.E. Knuth, The Art of Computer Programming, 2nd ed., vol. I, Addison-Wesley, New York, 1973.
17. J.G. Penaud, Une nouvelle bijection pour les animaux dirigés, Actes du 22ème Séminaire Lotharingien de Combinatoire, Publi. IRMA, Université Strasbourg 1 (1989).
18. J.G. Penaud, Animaux et arbres guingois, Theoret. Comput. Sci. 117 (1993) 67-89.
19. X.G. Viennot, A Survey of polyomino enumeration, in: P. Leroux, C. Reutenauer (Eds.), Proc. 4th FPSAC, Publications du LACIM 11, Université du Québec à Montréal, 1992, pp. 399-420.
20. J. West, Generating trees and forbidden subsequences, Discrete Math. (157) (1996) 363-374.