Methods of Enumerating Two Vertex Maps of Arbitrary Genus
Combinatorics
2017-02-09 v1
Abstract
This paper provides an alternate proof to parts of the Goulden-Slofstra formula for enumerating two vertex maps by genus, which is an extension of the famous Harer-Zagier formula that computes the Euler characteristic of the moduli space of curves. This paper also shows a further simplification to the Goulden-Slofstra formula. Portions of this alternate proof will be used in a subsequent paper, where it forms a basis for a more general result that applies for a certain class of maps with an arbitrary number of vertices.
Keywords
Cite
@article{arxiv.1702.02305,
title = {Methods of Enumerating Two Vertex Maps of Arbitrary Genus},
author = {Aaron Chun Shing Chan},
journal= {arXiv preprint arXiv:1702.02305},
year = {2017}
}