Abstract

ARDILA, FEDERICO. Semimatroids and their Tutte polynomials. Rev.colomb.mat. [online]. 2007, vol.41, n.1, pp.39-66. ISSN 0034-7426.

We define and study semimatroids, a class of objects which abstracts the dependence properties of an affine hyperplane arrangement. We show that geometric semilattices are precisely the posets of flats of semimatroids. We define and investigate the Tutte polynomial of a semimatroid. We prove that it is the universal Tutte-Grothendieck invariant for semimatroids, and we give a combinatorial interpretation for its non-negative integer coefficients.

Keywords : Semimatroid; pointed matroid; geometric semilattice; hyperplane arrangement; Tutte polynomial.

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