The uniform Gardner conjecture and rounding Borel flows
Logic
2022-12-08 v1 Combinatorics
Dynamical Systems
Abstract
We study groups which satisfy Gardner's equidecomposition conjecture for uniformly distributed sets. We prove that an amenable group has this property if and only if it does not admit as a quotient by a finite subgroup. Our technical contribution is an algorithm for rounding Borel flows for actions of amenable groups.
Cite
@article{arxiv.2212.03785,
title = {The uniform Gardner conjecture and rounding Borel flows},
author = {Matthew Bowen and Gábor Kun and Marcin Sabok},
journal= {arXiv preprint arXiv:2212.03785},
year = {2022}
}
Comments
9 pages. Split from arXiv:2106.01988v1