Simple formulas for lattice paths avoiding certain periodic staircase boundaries
Combinatorics
2008-05-07 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0705.2888,
title = {Simple formulas for lattice paths avoiding certain periodic staircase boundaries},
author = {Robin J. Chapman and Timothy Y. Chow and Amit Khetan and David Petrie Moulton and Robert J. Waters},
journal= {arXiv preprint arXiv:0705.2888},
year = {2008}
}