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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$n\rightarrow \infty$.doi:10.1017/s0004972716000174 fatcat:qidlnorw5ng7rnpyiht3lyy6ve