An abstract duality.

*(English)*Zbl 0686.05014The 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.

Reviewer: J.M.S.Simões Pereira

##### MSC:

05B99 | Designs and configurations |

05B35 | Combinatorial aspects of matroids and geometric lattices |

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\textit{R. G. Bland} and \textit{B. L. Dietrich}, Discrete Math. 70, No. 2, 203--208 (1988; Zbl 0686.05014)

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##### References:

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