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arXiv · 2602.09908

On the minimum number of entries in a pair of maximal orthogonal partial Latin squares

Diane M. Donovan·Mike Grannell·Emine Şule Yazıcı
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Abstract

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.

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Diane M. Donovan, Mike Grannell, Emine Şule Yazıcı. 2026-02-10. On the minimum number of entries in a pair of maximal orthogonal partial Latin squares. https://arxiv.org/abs/2602.09908

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