Arithmetic matroids, Tutte polynomial, and toric arrangements

Details Arithmetic matroids, Tutte polynomial, and toric arrangements Arithmetic matroids, Tutte polynomial, and toric arrangements

2011-05-16

arxiv.org/abs/1105.3220v3

Mathematics

Combinatorics

32 pages. Several mistakes corrected

Scientific paper

We introduce the notion of an arithmetic matroid, whose main example is given by a list of elements of a finitely generated abelian group. In particular we study the representability of its dual, providing an extension of the Gale duality to this setting. Guided by the geometry of generalized toric arrangements, we provide a combinatorial interpretation of the associated arithmetic Tutte polynomial, which can be seen as a generalization of Crapo's formula for the classical Tutte polynomial.

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