Limits of Latin squares

0583490 - MÚ 2024 RIV GB eng J - Journal Article
Garbe, Frederik - Hancock, Robert - Hladký, Jan - Sharifzadeh, M.
Limits of Latin squares.
Discrete Analysis. Roč. 2023, 20 July (2023), č. článku 8. ISSN 2397-3129
R&D Projects: GA ČR(CZ) GJ18-01472Y
Institutional support: RVO:67985840
Keywords : graphon * Latin square * Latinon * limits of discrete structures
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/11104/0351450