Cycle Structures of Autotopisms of Latin Squares of Order up to \(11\)

Abstract

The cycle structure of a Latin square autotopism \(\Theta = (\alpha, \beta, \gamma)\) is the triple \((I_\alpha,I_\beta, I_\gamma)\), where \(I_\delta\) is the cycle structure of \(\delta\), for all \(\delta \in \{\alpha, \beta, \gamma\}\). In this paper, we study some properties of these cycle structures and, as a consequence, we give a classification of all autotopisms of the Latin squares of order up to \(11\).