On the enumeration of labelled hypertrees and of labelled bipartite trees
Roland Bacher (IF)
TL;DR
This paper derives a straightforward formula for counting labelled hypertrees with specified hyperedge sizes and vertex degrees, and extends it to bipartite trees with prescribed degrees in each vertex class.
Contribution
It introduces a simple enumeration formula for labelled hypertrees and bipartite trees with given degree sequences, generalizing previous counting methods.
Findings
Derived a formula for counting hypertrees with fixed hyperedge sizes and degrees.
Extended the formula to count bipartite trees with prescribed degrees.
Simplified the enumeration process for these combinatorial structures.
Abstract
We give a simple formula for the number of hypertrees with hyperedges of given sizes and labelled vertices with prescribed degrees. A slight generalization of this formula counts labelled bipartite trees with prescribed degrees in each class of vertices.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications · Topological and Geometric Data Analysis