Schur's colouring theorem for non-commuting pairs
Combinatorics
2019-11-11 v2
Abstract
For G a finite non-Abelian group we write c(G) for the probability that two randomly chosen elements commute and k(G) for the largest integer such that any k(G)-colouring of G is guaranteed to contain a monochromatic quadruple (x,y,xy,yx) with xy not equal to yx. We show that c(G) tends to 0 if and only if k(G) tends to infinity.
Cite
@article{arxiv.1901.01738,
title = {Schur's colouring theorem for non-commuting pairs},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:1901.01738},
year = {2019}
}
Comments
7pp; corrected typos