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Limits of Latin squares
- Source :
- Discrete Analysis 2023:8
- Publication Year :
- 2020
-
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.<br />Comment: 66 pages, 1 figure, final version published in Discrete Analysis
- Subjects :
- Mathematics - Combinatorics
05B15
Subjects
Details
- Database :
- arXiv
- Journal :
- Discrete Analysis 2023:8
- Publication Type :
- Report
- Accession number :
- edsarx.2010.07854
- Document Type :
- Working Paper