Enumerating Acyclic Digraphs by Descents
Kassie Archer, Christina Graves
TL;DR
This paper develops a recurrence relation to count labeled acyclic digraphs based on the number of descents, providing a new combinatorial enumeration method.
Contribution
It introduces a recurrence formula for enumerating labeled acyclic digraphs by descents, advancing combinatorial enumeration techniques.
Findings
Derived a recurrence for counting acyclic digraphs by descents
Provided a systematic way to enumerate such digraphs
Enhanced understanding of the structure of acyclic digraphs
Abstract
A descent of a labeled acyclic digraph is a directed edge with . In this paper, we find a recurrence for the number of labeled acyclic digraphs with a given number of descents.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Combinatorial Mathematics · Graph theory and applications