THERE ARE ASYMPTOTICALLY THE SAME NUMBER OF LATIN SQUARES OF EACH PARITY

Abstract

A Latin square is reduced if its first row and first column are in natural order. For Latin squares of a particular order$n$, there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality between the numbers of reduced Latin squares of each possible parity as the order$n\rightarrow \infty$.