Semimatroids and their Tutte polynomials

Abstract

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.

27 pages, 3 figures

References in corpus (1)

• Totally frustrated states in the chromatic theory of gain graphs

Cited by in corpus (5)

• A Tutte polynomial for toric arrangements
• Stanley-Reisner rings for symmetric simplicial complexes, G-semimatroids and Abelian arrangements
• Finitary affine oriented matroids
• A Blass-Sagan bijection on Eulerian equivalence classes
• Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species