PARTIALLY ORDERED SETS WITH SELF COMPLEMENTARY COMPARABILITY-GRAPHS

A 2-poset (X, {P, Q}) is a pair consisting of a set X and a set {P, Q} of two partial order relations on X such that any two distinct elements of X are comparable in exactly one of these relations. We consider 2-posets (X, {P, Q} with the property that there exists an order-isomorphism f:(X, P) --> (X, Q). Thus the poset (X, P) has the property that its comparability graph is self-complementary. We derive results about the structure of such 2-posets, and we determine properties of the order-isomorphism f.