Hultman numbers, polygon gluings and matrix integrals
arXiv:1111.3061
Abstract
The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the Hultman numbers: in terms of polygon gluings and as integrals over the space of complex matrices, and derive some properties of their generating functions.
9 pages, 2 figures