The numbers of distinct self-orthogonal Latin squares (SOLS) and idempotent SOLS have been enumerated for orders up to and including 9. The isomorphism classes of idempotent SOLS have also been enumerated for these orders. However, the enumeration of the isomorphism classes of non-idempotent SOLS is still an open problem. By utilising the automorphism groups of class representatives from the al...

We have earlier reported the MOLSDOCK technique to perform rigid receptor/flexible ligand docking. The method uses the MOLS method, developed in our laboratory. In this paper we report iMOLSDOCK, the 'flexible receptor' extension we have carried out to the algorithm MOLSDOCK. iMOLSDOCK uses mutually orthogonal Latin squares (MOLS) to sample the conformation and the docking pose of the ligand an...

Since 1782, when Euler addressed the question of existence of a pair of Orthogonal Latin Squares (OLS) by stating his famous conjecture ([8, 9, 13]), these structures have remained an active area of research due to their theoretical properties as well as their applications in a variety of fields. In the current work we consider the polyhedral aspects of OLS. In particular we establish the dimen...

Let J∗(v) be the set of all integers k such that there is a pair of Latin squares L and L′ with their own orthogonal mates on the same v-set, and with L and L′ having k cells in common. In this article we completely determine the set J∗(v) for integers v ≥ 24 and v = 1, 3, 4, 5, 8, 9. For v = 7 and 10 ≤ v ≤ 23, there are only a few cases left undecided for the set J∗(v).