Simple formulas for lattice paths avoiding certain periodic staircase boundaries

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Chapman, Robin J.
Chow, Timothy Y.
Khetan, Amit
Moulton, David Petrie
Waters, Robert J.
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Abstract
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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.
Comment: Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new refs added
Keywords
Mathematics - Combinatorics, 05A15
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