Semimatroids and their Tutte polynomials

Details Semimatroids and their Tutte polynomials Semimatroids and their Tutte polynomials

2004-08-31

arxiv.org/abs/math/0409003v1

Mathematics

Combinatorics

27 pages, 3 figures

Scientific paper

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 coefficients.

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