Geodesic
Arithmetic matroids and Tutte polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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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. 
@article{DMTCS_2012_special_263_a29,
     author = {D'Adderio, Michele and Moci, Luca},
     title = {Arithmetic matroids and {Tutte} polynomials},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3043/}
}
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%A Moci, Luca
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%J Discrete mathematics & theoretical computer science
%D 2012
%V DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
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D'Adderio, Michele; Moci, Luca. Arithmetic matroids and Tutte polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3043. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3043/

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