2013/01/31 by Ira M. Gessel, Gessel, Ira M., Walter Shur +1
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.1301.7714
arxiv created 2013/01/31 · arxiv updated 2013/02/01
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.