A fixed-point theorem for face maps, or deletion-tolerant random finite sets
Group Theory
2026-04-01 v2 Combinatorics
Dynamical Systems
Abstract
We establish a fixed-point theorem for the face maps that consist in deleting the th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions. Consequences for various monoids of order-preserving transformations of are discussed in an appendix.
Cite
@article{arxiv.2505.21484,
title = {A fixed-point theorem for face maps, or deletion-tolerant random finite sets},
author = {Tom Hutchcroft and Nicolas Monod and Omer Tamuz},
journal= {arXiv preprint arXiv:2505.21484},
year = {2026}
}
Comments
Streamlined the proof of Theorem A, added comments on Folner sets, and added an appendix on order-preserving maps of N