Limits of Latin squares
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910696558559232 |
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| author | Garbe, Frederik Hancock, Robert Hladký, Jan Sharifzadeh, Maryam |
| author_facet | Garbe, Frederik Hancock, Robert Hladký, Jan Sharifzadeh, Maryam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_07854 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Limits of Latin squares Garbe, Frederik Hancock, Robert Hladký, Jan Sharifzadeh, Maryam Combinatorics 05B15 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. |
| title | Limits of Latin squares |
| topic | Combinatorics 05B15 |
| url | https://arxiv.org/abs/2010.07854 |