English

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}
}