Regular Mates of Power Squares

Undergraduate: Christopher DeFiglia

Faculty Advisor: Carl Mummert
Department: Mathematical Decision Science

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We study the number of mates of latin squares which are powers of cyclic squares. For k > 1 the cyclic square C_k is the Cayley table of Z_k. The power square (C_k)^n is obtained by taking a repeated Kronecker product of C_k with itself. In this work, we consider the power squares (C_k)^n for k > 2 and n > 1. For each of these squares, we enumerate a family of mates of a particular form. This gives an asymptotic lower bound for the number of mates that a latin square can have in terms of its size.