Further results on latin squares with disjoint subsquares using rational outline squares
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908910974140416 |
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| author | Kemp, Tara Lefevre, James |
| author_facet | Kemp, Tara Lefevre, James |
| contents | In this paper we consider the problem of finding latin squares with sets of pairwise disjoint subsquares. We develop a new necessary condition on the sizes of the subsquares which incorporates and extends the known conditions. We provide a construction for the case where all but two of the subsquares are the same size, and in this case the condition is sufficient. We obtain these results using symmetric rational outline squares, and additionally provide several new results and extensions to this theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Further results on latin squares with disjoint subsquares using rational outline squares Kemp, Tara Lefevre, James Combinatorics 05B15 In this paper we consider the problem of finding latin squares with sets of pairwise disjoint subsquares. We develop a new necessary condition on the sizes of the subsquares which incorporates and extends the known conditions. We provide a construction for the case where all but two of the subsquares are the same size, and in this case the condition is sufficient. We obtain these results using symmetric rational outline squares, and additionally provide several new results and extensions to this theory. |
| title | Further results on latin squares with disjoint subsquares using rational outline squares |
| topic | Combinatorics 05B15 |
| url | https://arxiv.org/abs/2505.07252 |