A bijection for Delannoy paths

preprint2022arXivOpen access

Abstract

We exhibit a bijection between central Delannoy nn-paths, that is, lattice paths from the origin to (n,n)(n,n) with steps E=(1,0), N=(0,1), D=(1,1)E=(1,0), \,N=(0,1),\,D=(1,1) and the lattice paths from the origin to (n+1,n)(n+1,n) where the only restriction on the steps is that they have finite nonnegative slope.

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