A lower bound for the size of the smallest critical set in the back circulant latin square

Abstract

The back circulant latin square of order n is the latin square based on the addition table for the integers modulo n. A critical set is a partial latin square that has a unique completion to a latin square, and is minimal with respect to this property. In this note we show that the size of a critical set in the back circulant latin square of order n is at least n ⁴/³/2 - n - n²/³/2 + 2n¹/³ - 1.