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

Abstract

The cycle structure of a Latin square autotopism Θ = (α, β, γ) is the triple (lα, lβ, lγ), where lδ is the cycle structure of δ, for all δ ∈ {α, β, γ}. 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.