Matrix integrals and generating functions for permutations and one-face rooted hypermaps
Combinatorics
2015-01-28 v2 Mathematical Physics
math.MP
Abstract
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum system. A recursion relation for these generating functions is also found. The method for computing similar generating functions for two-face rooted hypermaps by number of vertices and edges is outlined.
Cite
@article{arxiv.1407.7774,
title = {Matrix integrals and generating functions for permutations and one-face rooted hypermaps},
author = {Jacob P. Dyer},
journal= {arXiv preprint arXiv:1407.7774},
year = {2015}
}
Comments
19 pages, 4 figures