Counting Labelled Trees with Given Indegree Sequence

Rosena R. X. Du, Jingbin Yin

For a labelled tree on the vertex set $[n]:=\{1,2,...,n\}$, define the direction of each edge $ij$ to be $i\to j$ if $i<j$. The indegree sequence of $T$ can be considered as a par…