An introduction to SDR’s and Latin squares

In this paper we study systems of distinct representatives (SDR’s) and Latin squares, considering SDR’s especially in their application to constructing Latin squares. We give proofs of several important elementary results for SDR’s and Latin squares, in particular Hall’s marriage theorem and lower bounds for the number of Latin squares of each order, and state several other results, such as necessary and sufficient conditions for having a common SDR for two families. We consider some of the applications of Latin squares both in pure mathematics, for instance as the multiplication table for quasigroups, and in applications, such as analyzing crops for differences in fertility and susceptibility to insect attack. We also present a brief history of the study of Latin squares and SDR’s.