Simple formulas for lattice paths avoiding certain periodic staircase boundaries

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

There is a strikingly simple classical formula for the number of lattice paths avoiding the line x = ky when k is a positive integer. We show that the natural generalization of this simple formula continues to hold when the line x = ky is replaced by certain periodic staircase boundaries--but only under special conditions. The simple formula fails in general, and it remains an open question to what extent our results can be further generalized.
Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new refs added

Keywords

Combinatorics, 05A15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/160358

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.2888
 http://arxiv.org/abs/0705.2888

Collections

arXiv