On the enumeration of labelled hypertrees and of labelled bipartite trees

Abstract

We give a simple formula for the number of hypertrees with $k$ hyperedges of given sizes and $n+1$ labelled vertices with prescribed degrees. A slight generalization of this formula counts labelled bipartite trees with prescribed degrees in each class of vertices.

typo in formula (7) corrected

Cited by in corpus (2)

• Spanning trees in random regular uniform hypergraphs
• Hypertree posets and hooked partitions