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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09908 |
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| _version_ | 1866917264111960064 |
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| author | Donovan, Diane M. Grannell, Mike Yazıcı, Emine Şule |
| author_facet | Donovan, Diane M. Grannell, Mike Yazıcı, Emine Şule |
| contents | It is shown that if $F$ denotes the number of filled cells in a superimposed pair of maximal orthogonal partial Latin squares of order $n$, then $F\ge n^2/3$. This resolves a conjecture raised in an earlier paper by the current authors. It is also shown that, for $n\ge 21$, the least possible number of filled cells in a pair of maximal orthogonal partial Latin squares is $\lceil n^2/3 \rceil$, and that the structure that achieves this bound is unique up to permutations of rows, columns and entries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the minimum number of entries in a pair of maximal orthogonal partial Latin squares Donovan, Diane M. Grannell, Mike Yazıcı, Emine Şule Combinatorics 05B15 (Primary), 94B65 (secondary) It is shown that if $F$ denotes the number of filled cells in a superimposed pair of maximal orthogonal partial Latin squares of order $n$, then $F\ge n^2/3$. This resolves a conjecture raised in an earlier paper by the current authors. It is also shown that, for $n\ge 21$, the least possible number of filled cells in a pair of maximal orthogonal partial Latin squares is $\lceil n^2/3 \rceil$, and that the structure that achieves this bound is unique up to permutations of rows, columns and entries. |
| title | On the minimum number of entries in a pair of maximal orthogonal partial Latin squares |
| topic | Combinatorics 05B15 (Primary), 94B65 (secondary) |
| url | https://arxiv.org/abs/2602.09908 |