Simple formulas for lattice paths avoiding certain periodic staircase boundaries

Details Simple formulas for lattice paths avoiding certain periodic staircase boundaries Simple formulas for lattice paths avoiding certain periodic staircase boundaries

2007-05-20

arxiv.org/abs/0705.2888v2

Mathematics

Combinatorics

Accepted version (JCTA); proof of Corollary 7 expanded, and 2 new refs added

Scientific paper

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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