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Some Relations on Paratopisms and An Intuitive Interpretation on the Adjugates of a Latin Square
This paper will present some intuitive interpretation of the adjugate
transformations of arbitrary Latin square. With this trick, we can generate the
adjugates of arbitrary Latin square directly from the original one without
generating the orthogonal array. The relations of isotopisms and adjugate
transformations in composition will also be shown. It will solve the problem
that when F1*I1=I2*F2 how can we obtain I2 and F2 from I1 and F1, where I1 and
I2 are isotopisms while F1 and F2 are adjugate transformations and * is the
composition. These methods could distinctly simplify the computation on a
computer for the issues related to main classes of Latin squares.Comment: Any comments and criticise are appreciate