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Between Broadway and the Hudson: A Bijection of Corridor Paths (2006.06516v3)
Published 11 Jun 2020 in math.CO and cs.DM
Abstract: We present a substantial generalization of the equinumeracy of grand Dyck paths and Dyck-path prefixes, constrained within a band. The number of constrained paths starting at level $i$ and ending in a window of size $2j+2$ is equal to the number starting at level $j$ and ending in a window of size $2i+2$ centered around the same point. A new encoding of lattice paths provides a bijective proof.