Even and Odd Pairs of Lattice Paths with Multiple Intersections
Combinatorics
2013-02-01 v1
Abstract
Let M(n,k,r,s) be the number of ordered paths in the plane, with unit steps E or N, that intersect k times in which the first path ends at the point (r,n-r) and the second path ends at the point (s,n-s). Our main object of study in this paper is the sum of the numbers M(n,k,r,s) over r and s where r+s is fixed. We consider even and odd values of r+s separately, and we derive a simpler formula for M(n,k,r,s) than previously appeared in the literature.
Cite
@article{arxiv.1301.7714,
title = {Even and Odd Pairs of Lattice Paths with Multiple Intersections},
author = {Ira M. Gessel and Walter Shur},
journal= {arXiv preprint arXiv:1301.7714},
year = {2013}
}