Limits of Latin Squares

0573950 - ÚI 2024 RIV GB eng J - Journal Article
Garbe, F. - Hancock, R. - Hladký, Jan - Sharifzadeh, M.
Limits of Latin Squares.
Discrete Analysis. Roč. 8, July 2023 (2023), č. článku da.83253. ISSN 2397-3129
Institutional support: RVO:67985807
Keywords : Latin square * Latinon * limits of discrete structures * graphon
OECD category: Pure mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Open access
https://dx.doi.org/10.19086/da.83253

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.
Permanent Link: https://hdl.handle.net/11104/0344331


Research data: ArXiv.org