This paper considers combinatorial interpretations for two triangular recurrence arrays containing the Schröder numbers sn = 1, 1, 3, 11, 45, 197, ... and rn = 1, 2, 6, 22, 90, 394, ... , for n = 0, 1, 2, .... These interpretations involve the enumeration of constrained lattice paths and bicolored parallelogram polyominoes, called zebras. In addition to two recent inductive constructions of zebras and their associated generating trees, we present two new ones and a bijection between zebras and constrained lattice paths. We use the constructions with generating function methods to count sets of zebras with respect to natural parameters.
Schroeder trinagles, paths, and parallelogram polyominoes / E. Pergola; R. A. Sulanke. - In: JOURNAL OF INTEGER SEQUENCES. - ISSN 1530-7638. - ELETTRONICO. - (1998), pp. 0-0.
Schroeder trinagles, paths, and parallelogram polyominoes
PERGOLA, ELISA;
1998
Abstract
This paper considers combinatorial interpretations for two triangular recurrence arrays containing the Schröder numbers sn = 1, 1, 3, 11, 45, 197, ... and rn = 1, 2, 6, 22, 90, 394, ... , for n = 0, 1, 2, .... These interpretations involve the enumeration of constrained lattice paths and bicolored parallelogram polyominoes, called zebras. In addition to two recent inductive constructions of zebras and their associated generating trees, we present two new ones and a bijection between zebras and constrained lattice paths. We use the constructions with generating function methods to count sets of zebras with respect to natural parameters.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.