✦ LIBER ✦

Enumeration of Hypergraphs

✍ Scribed by Toru Ishihara

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 87 KB
Volume: 22
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2001.0498

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we will study enumeration of hypergraphs. Let S p be a symmetric group acting on a p-setX . It induces the permutation group S * p acting on the set of all subsets of X . Our problem is reduced to finding a good formula for the cycle index of S * p . A crucial point is to calculate the cycle inventory of the permutation induced by a single cycle. Their formulas are given inductively. We will give the cycle index of S * p explicitly and concretely. We will find a relation between the cycle inventory of the induced permutation and the number of convex k-gons of a given regular p-gon and obtain the formula for its cycle inventory.

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