Between Broadway and the Hudson: A Bijection of Corridor Paths
share
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.
READ FULL TEXT