Hypergraphs and a functional equation of Bouwkamp and de Bruijn
Combinatorics
2013-04-02 v1
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.
Keywords
Cite
@article{arxiv.math/0410373,
title = {Hypergraphs and a functional equation of Bouwkamp and de Bruijn},
author = {Ira M. Gessel and Louis H. Kalikow},
journal= {arXiv preprint arXiv:math/0410373},
year = {2013}
}
Comments
16 pages. To appear in J. Combin. Theory Ser. A