Latin trades on three or four rows Original Research Article

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.