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

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

2007-09-19

arxiv.org/abs/0709.2973v2

Mathematics

Combinatorics

18 pages. Accepted for publication in Ars Combinatoria

Scientific paper

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.

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