Some Relations on Paratopisms and An Intuitive Interpretation on the Adjugates of a Latin Square

Abstract: 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 of transformations. These methods could distinctly simplify the computation on a computer for the issues related to main classes of Latin squares. This will improve the efficiency apparently in computation for some related problems.