Approximate counting of regular hypergraphs

TL;DR

This paper develops an asymptotic counting method for d-regular k-uniform hypergraphs on n vertices, extending existing techniques to hypergraphs with certain degree constraints.

Contribution

It introduces an extension of McKay and Wormald's switching technique to hypergraphs for asymptotic enumeration under degree constraints.

Findings

Derived asymptotic formulas for counting hypergraphs

Extended switching techniques to hypergraph enumeration

Applicable for fixed k and degree d=o(n^{1/2})

Abstract

In this paper we asymptotically count $d$-regular $k$-uniform hypergraphs on $n$ vertices, provided $k$ is fixed and $d=d(n)=o(n^{1/2})$. In doing so, we extend to hypergraphs a switching technique of McKay and Wormald.