When R is a partial identity relation, difunctional, or a block diagonal relation, then fringe(R) = R. Otherwise the fringe operator selects a boundary sub-relation described in terms of its logical matrix: fringe(R) is the side diagonal if R is an upper right triangular linear order or strict order. Fringe(R) is the block fringe if R is irreflexive (R \subseteq \bar{I}) or upper right block triangular. Fringe(R) is a sequence of boundary rectangles when R is of Ferrers type.
