Enumerating Partial Duals of Hypermaps by Genus
Combinatorics
2025-01-22 v1
Abstract
The concept of partial duality in hypermaps was introduced by Chmutov and Vignes-Tourneret, and Smith independently. This notion serves as a generalization of the concept of partial duality found in maps. In this paper, we first present an Euler-genus formula concerning the partial duality of hypermaps, which serves as an invariant related to the result obtained by Chmutov and Vignes-Tourneret. This formulation also generalizes the result of Gross, Mansour, and Tucker regarding partial duality in maps. Subsequently, we enumerate the distribution of partial dual Euler-genus for hypermaps and compute the corresponding polynomial for specific classes of hypermaps through three operations: join, bar-amalgamation, and subdivision.
Cite
@article{arxiv.2501.11215,
title = {Enumerating Partial Duals of Hypermaps by Genus},
author = {Wenwen Liu and Yichao Chen},
journal= {arXiv preprint arXiv:2501.11215},
year = {2025}
}