A representation-theoretic computation of the rank of $1$-intersection incidence matrices: $2$-subsets vs. $n$-subsets

Joshua E. Ducey, Colby J. Sherwood

Let $W_{k,n}^i(m)$ denote a matrix with rows and columns indexed by the $k$-subsets and $n$-subsets, respectively, of an $m$-element set. The row $S$, column $T$ entry of $W_{k,n…