论文信息 - An alternative method for q-counting directed column-convex polyominoes

An alternative method for q-counting directed column-convex polyominoes

Abstract The area+perimeter generating function of directed column-convex polyominoes will be written as a quotient of two expressions, each of which involves powers of q of all kinds: positive, zero and negative. The method used in the proof applies to some other classes of column-convex polyominoes as well. At least occasionally, that method can do the case q =1 too.

Svjetlan Feretic | S. Feretic

[1] Renzo Sprugnoli,et al. A Characterization of Binary Search Networks , 1991, FCT.

[2] K. Lin,et al. Rigorous results for the number of convex polygons on the square and honeycomb lattices , 1988 .

[3] Emil Grosswald,et al. The Theory of Partitions , 1984 .

[4] George Polya,et al. On the number of certain lattice polygons , 1969 .

[5] Mireille Bousquet-Mélou,et al. A method for the enumeration of various classes of column-convex polygons , 1996, Discret. Math..

[6] M. Delest,et al. Enumeration of Directed Column-Convex Animals with a Given Perimeter and Area , 1993 .

[7] Mireille Bousquet-Mélou,et al. Empilements de segments et q-énumération de polyominos convexes dirigés , 1992, J. Comb. Theory, Ser. A.

[8] Isabelle Dutour. Grammaires d'objets : énumération, bijections et génération aléatoire , 1996 .

[9] Ronald L. Rivest,et al. Asymptotic bounds for the number of convex n-ominoes , 1974, Discret. Math..

[10] Marie-Pierre Delest,et al. Generating functions for column-convex polyominoes , 1988, J. Comb. Theory, Ser. A.

[11] Ira M. Gessel,et al. A noncommutative generalization and $q$-analog of the Lagrange inversion formula , 1980 .

[12] Mireille Bousquet-Mélou,et al. Codage des polyominos convexes et équations pour l'énumération suivant l'aire , 1994, Discret. Appl. Math..