Enumeration of k-Exceedance Lattice Paths with an Application to Comparing Chains of Order Statistics

Charles Hoffman, Corey Manack

We enumerate the number of monotonic lattice paths starting at $(0,0)$ and terminating at $(m,n)$ in which $l$ of the first $k$ steps lie below the line $y=x\ (0\leq k\leq m\leq n)…