Cycle structures of autotopisms of the Latin squares of order up to 11

Abstract

The cycle structure of a Latin square autotopism $\Theta=(\alpha,\beta,\gamma)$ is the triple $(\mathbf{l}_{\alpha},\mathbf{l}_{\beta},\mathbf{l}_{\gamma})$, where $\mathbf{l}_{\delta}$ 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.