Parity Types, Cycle Structures and Autotopisms of Latin Squares

  • Daniel Kotlar
Keywords: Latin square, parity type, cycle structure, autotopy group


The parity type of a Latin square is defined in terms of the numbers of even and odd rows and columns. It is related to an Alon-Tarsi-like conjecture that applies to Latin squares of odd order. Parity types are used to derive upper bounds for the size of autotopy groups. A new algorithm for finding the autotopy group of a Latin square, based on the cycle decomposition of its rows, is presented, and upper bounds for the size of autotopy groups are derived from it.
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