On the number of symmetric Latin squares

Abstract

The number of symmetric Latin squares is closely related with the security of the post-commutative quasigroups cipher. Let L n denote the number of distinct n×n Latin squares. It is fairly well known that equation and asymptotically L n ∼ (n over e)n2 as n ₒ ∞. Let S n denote the number of distinct n × n symmetric Latin squares. In this paper, we give a lower bound of S n and show that equation (n → ∞) when n is odd, and equation (n → ∞) when n is even.