An abstract duality (Q1262319)

The paper deals with a concept of abstract duality defined on a family of structures (matroids, Sperner families, oriented matroids, for instance) as a correspondence among members of the family that is an involution, preserve the ground set and interchanges contractions and deletions. The uniqueness of such a correspondence for several structures is discussed. For a more detailed study of the proofs, the authors refer to the Ph. D. thesis of the second named and a joint technical report published by the Cornell University School of OR/IE (No.726) and IBM (No.12527) in 1986 and 1987, respectively.