English

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}
}
R2 v1 2026-06-21T23:57:03.138Z