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arXiv · 2408.12874

Enumeration of dihypergraphs with specified degrees and edge types

Catherine Greenhill·Tamás Makai
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Abstract

A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical reactions or relational databases. We provide asymptotic formulae for the number of directed hypergraphs with given in-degree sequence, out-degree sequence, and with the head and tail sizes of all hyperarcs specified. Our formulae hold when none of the following parameters are too large: the maximum out-degree, the maximum in-degree, the maximum head size and the maximum tail size.

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Catherine Greenhill, Tamás Makai. 2024-08-23. Enumeration of dihypergraphs with specified degrees and edge types. https://arxiv.org/abs/2408.12874

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