Constraints for Breaking All Row and Column Symmetries in a Three-by-Two Matrix

Constraint programs containing a matrix of two (or more) dimensions of decision variables often have row and column symmetries: in any assignment to the variables, the values assigned to any two rows can be swapped and the values assigned to any two columns can be swapped without affecting whether or not the assignment is a solution. This introduces an enormous amount of redundancy when searching a space of partial assignments. It has been shown previously that one can remove some, but not all, of these symmetries by extending such a program with constraints that require the rows and columns to be lexicographically ordered. This paper identifies a fully-simplified set of constraints that breaks all row and column symmetry in a matrix with three columns and two rows.