Eulerian Polynomials for Digraphs

Kyle Celano, Nicholas Sieger, Sam Spiro

Given an $n$-vertex digraph $D$ and a labeling $\sigma :V(D)\to [n]$, we say that an arc $u\to v$ of $D$ is a descent of $\sigma$ if $\sigma (u)>\sigma (v)$. Foata and Zeilberger introduced a generating…