English

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 (Z/2Z)(Z/2Z)(\mathbb{Z}/2\mathbb{Z}) *(\mathbb{Z}/2\mathbb{Z}) as a quotient by a finite subgroup. Our technical contribution is an algorithm for rounding Borel flows for actions of amenable groups.

Keywords

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

R2 v1 2026-06-28T07:24:58.716Z