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.

arXiv comment18 pages. Accepted for publication in Ars Combinatoria

Cited by in corpus (3)

• The set of autotopisms of partial Latin squares
• Autoparatopisms of Quasigroups and Latin Squares
• Computing autotopism groups of partial Latin rectangles: a pilot study