A coarse Tutte polynomial for hypermaps
Combinatorics
2024-08-12 v2
Abstract
We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions where the terminal forms consist of isolated vertices. Our Tutte polynomial extends the classical Tutte polynomial of a graph as well as the Tutte polynomial of an embedded graph (i.e., the ribbon graph polynomial), and it is a specialization of the transition polynomial via a medial map transformation. We give hypermap duality and partial duality identities for our polynomial, as well as some evaluations, and examine relations between our polynomial and other hypermap polynomials.
Cite
@article{arxiv.2404.00194,
title = {A coarse Tutte polynomial for hypermaps},
author = {Joanna A. Ellis-Monaghan and Iain Moffatt and Steven Noble},
journal= {arXiv preprint arXiv:2404.00194},
year = {2024}
}