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Hypergraphs and a functional equation of Bouwkamp and de Bruijn

Ira M. Gessel, Louis H. Kalikow

Published 2004-10-17Version 1

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.

Comments: 16 pages. To appear in J. Combin. Theory Ser. A
Journal: Hypergraphs, hypertrees, and expansions of some formal power series, J. Combin. Theory Ser. A 110 (2005), 275-289
Categories: math.CO
Subjects: 05A15
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