Limits of Latin squares
Combinatorics
2024-11-15 v3
Abstract
We develop a limit theory of Latin squares, paralleling the recent limit theories of dense graphs and permutations. We introduce a notion of density, an appropriate version of the cut distance, and a space of limit objects - so-called Latinons. Key results of our theory are the compactness of the limit space and the equivalence of the topologies induced by the cut distance and the left-convergence. Last, using Keevash's recent results on combinatorial designs, we prove that each Latinon can be approximated by a finite Latin square.
Keywords
Cite
@article{arxiv.2010.07854,
title = {Limits of Latin squares},
author = {Frederik Garbe and Robert Hancock and Jan Hladký and Maryam Sharifzadeh},
journal= {arXiv preprint arXiv:2010.07854},
year = {2024}
}
Comments
66 pages, 1 figure, final version published in Discrete Analysis