Abstract :
Latin trades are closely related to the problem of critical sets in Latin squares. We denote the cardinality of the smallest critical set in any Latin square of order n by image. A consideration of Latin trades which consist of just two columns, two rows, or two elements establishes that image. We conjecture that a consideration of Latin trades on four rows may establish that image. We look at various attempts to prove a conjecture of Cavenagh about such trades. The conjecture is proven computationally for values of n less than or equal to 9. In particular, we look at Latin squares based on the group table of image for small n and trades in three consecutive rows of such Latin squares.
