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.

D'Adderio M, Moci L (2012). Arithmetic matroids and Tutte polynomials.

Arithmetic matroids and Tutte polynomials

Moci L
2012

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.
2012
24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
325
336
D'Adderio M, Moci L (2012). Arithmetic matroids and Tutte polynomials.
D'Adderio M; Moci L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/676836
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