A new bound on the size of the largest critical set in a Latin square Original Research Article

A critical set in an n×n array is a set C of given entries, such that there exists a unique extension of C to an n×n Latin square and no proper subset of C has this property. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978, Curran and van Rees proved that lcs(n)⩽n2−n. Here, we show that lcs(n)⩽n2−3n+3.