2026/02/10 by Diane M. Donovan, Mike Grannell, Emine Şule Yazıcı · 1 voice
Mathematics · #math.CO
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≥ n2/3. This resolves a conjecture raised in an earlier paper by the current authors. It is also shown that, for n≥ 21, the least possible number of filled cells in a pair of maximal orthogonal partial Latin squares is \lceil n2/3 \rceil, and that the structure that achieves this bound is unique up to permutations of rows, columns and entries.