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arXiv · 0705.2888

Simple formulas for lattice paths avoiding certain periodic staircase boundaries

Robin J. Chapman·Timothy Y. Chow·Amit Khetan·David Petrie Moulton·Robert J. Waters
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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.

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Robin J. Chapman, Timothy Y. Chow, Amit Khetan, David Petrie Moulton, Robert J. Waters. 2008-05-07. Simple formulas for lattice paths avoiding certain periodic staircase boundaries. https://arxiv.org/abs/0705.2888

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