Geodesic
Almost all Latin squares have trivial autoparatopy group
Prikladnaâ diskretnaâ matematika, no. 3 (2009), pp. 29-32.

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The main result is: almost all Latin squares of order $n$ have trivial autoparatopy group as $n\to\infty$. As a consequence we obtain the asymptotic number of main classes of Latin squares of order $n$: $$ \frac{L_n}{6n!^3}(1+o(1)), $$ where $L_n$ – number of Latin squares of order $n$. 
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A. V. Cheremushkin. Almost all Latin squares have trivial autoparatopy group. Prikladnaâ diskretnaâ matematika, no. 3 (2009), pp. 29-32. http://geodesic.mathdoc.fr/item/PDM_2009_3_a3/

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