  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 fast algorithm for finding the
autotopy group of a Latin square, based on the cycle decomposition of its rows,
is presented.
