A new class of critical sets in Latin squares

Abstract

Previously the process of finding critical sets in Latin squares has been made cumbersome by the complexity and number of Latin trades that must, be constructed. In this paper we develop a theory of Latin trades that yields more, transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the, Latin square of order 2 with a back circulant Latin square of odd order. (Classification number: 05B15).