Counting Free Abelian Actions
Combinatorics
2013-04-11 v1
Abstract
We consider the problem of counting commuting r-tuples of elements of the symmetric group S_n, i.e. computing |Hom(Z^r,S_n)|. The cases r=1,2 are well-known; a product formula for the case r=3 was conjectured by Adams-Watters and later proved by Britnell. In this note we solve the problem for arbitrary r.
Keywords
Cite
@article{arxiv.1304.2830,
title = {Counting Free Abelian Actions},
author = {Tad White},
journal= {arXiv preprint arXiv:1304.2830},
year = {2013}
}