Arithmetic matroids and Tutte polynomials

Abstract

We introduce the notion of arithmetic matroid, whose main example is provided by a list of elements in a finitely generated abelian group. We study the representability of its dual, and, guided by the geometry of toric arrangements, we give a combinatorial interpretation of the associated arithmetic Tutte polynomial, which can be seen as a generalization of Crapo's formula.

Keywords

• arithmetic matroids
• gale duality
• tutte polynomial
• toric arrangements
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]