Hypergraphs and a functional equation of Bouwkamp and de Bruijn

Abstract

We show that a 1969 result of Bouwkamp and de Bruijn on a formal power series expansion can be interpreted as the hypergraph analogue of the fact that every connected graph with n vertices has at least n-1 edges. We explain some of Bouwkamp and de Bruijn's formulas in terms of hypertrees and we use Lagrange inversion to count hypertrees by the number of vertices and the number of edges of a specified size.