Phase transitions in infinitely generated groups, and related problems in additive number theory
Group Theory
2011-07-12 v1 Combinatorics
Abstract
Let A be an infinite set of generators for a group G, and let L_A(r) denote the number of elements of G whose word length with respect to A is exactly r. The purpose of this note is to determine all growth functions L_A(r) associated to infinite generating sets for groups, and to describe a phase transition phenomenon associated with infinite generating sets. A list of open problems is also.included.
Cite
@article{arxiv.0811.3990,
title = {Phase transitions in infinitely generated groups, and related problems in additive number theory},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:0811.3990},
year = {2011}
}
Comments
11 pages