On the minimum number of entries in a pair of maximal orthogonal partial Latin squares
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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Mathematics and Applications
Coding theory and cryptography
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 February 2026
- Language
- EN
- Document type
- Preprint