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Critical Sets For Latin Squares of Order \(7\)

Diane Donovan1, Adelle Howse 1
1Centre for Discrete Mathematics and Computing, Mathematics Department, The University of Queensland, Queensland, 4072, Australia

Abstract

This paper provides a general method for finding a critical set for any Latin square of order \(n\). This method is used to prove the existence of critical sets of various sizes. It has also been applied to all main classes of Latin squares of order seven, thereby producing a critical set for each Latin square of order seven.