¹San Francisco State University, Department of Mathematics, San Francisco CA, USA 94110, USA.
E-mail: federico@math.sfsu.edu

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.

Key words: Semimatroid, pointed matroid, geometric semilattice, hyperplane arrangement, Tutte polynomial.

En este artículo definimos y estudiamos las semimatroides, una clase de objetos que abstraen las propiedades de dependencia de un arreglo de hiperplanos afines. Demostramos que un semiretículo es geométrico si y sólo si es el semiretículo de conjuntos cerrados de una semimatroide. Definimos e investigamos el polinomio de Tutte de una semimatroide. Demostramos que es la invariante universal de Tutte-Grothendieck para la clase de semimatroides, y presentamos una interpretación combinatoria de sus coeficientes, que son enteros no negativos.

Palabras clave: Semimatroide, matroide, semiretículo geométrico, hiperplano afín, polinomio de Tutte.

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