Bijective recurrences concerning two Schröder triangles

Shishuo Fu, Yaling Wang

Let $r(n,k)$ (resp. $s(n,k)$) be the number of Schröder paths (resp. little Schröder paths) of length $2n$ with $k$ hills, and set $r(0,0)=s(0,0)=1$. We bijectively establish the f…