Work

Borel Combinatorics of Schreier Graphs of $\mathbb{Z}$-actions

Year: 2025

Type: preprint

Abstract: In this paper we consider the Borel combinatorics of Schreier graphs of $\mathbb{Z}$-actions with arbitrary finite generating sets. We focus mostly on the problem of computing the Borel chromatic numbers of the Schreier graphs on the free part of the shift space $2^\mathbb{Z}$ with a finite symmetric generating set $S$ of $\mathbb{Z}$. Our main results include some general lower and upper bounds, as well as the exact values in some special cases. These values are sometimes the same as the chromatic numbers of the distance graphs on $\mathbb{Z}$ given by $S$, and more often different from them.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.27290

Authors: Gao, Su, Jiang, Yingying, Wang, Tianhao

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Award: G2480368741

OpenAlex ID: W4415918739

Cites:

Cited by:

Related to: