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- W1993128541 abstract "There are two concepts of duality in combinatorial geometry. A set theoretical one, generalizing the structure of two orthocomplementary vector spaces, and a lattice theoretical concept of an adjoint, that mimics duality between points and hyperplanes. The latter — usually called polarity — seems to make sense almost only in the linear case. In fact the only non-linear combinatorial geometries known to admit an adjoint were of rank 3. Moreover, N.E. Mnëv conjectured that in higher ranks there would exist no non-linear oriented matroid that has an oriented adjoint. At least with unoriented matroids this is not true. In this paper we present a class of rank-4 matroids with adjoint including a non-linear example." @default.
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- W1993128541 date "1995-06-01" @default.
- W1993128541 modified "2023-09-27" @default.
- W1993128541 title "On pseudomodular matroids and adjoints" @default.
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- W1993128541 doi "https://doi.org/10.1016/0166-218x(94)00039-g" @default.
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