D'Adderio, Michele and Moci, Luca - Arithmetic matroids and Tutte polynomials

dmtcs:3043 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Arithmetic matroids and Tutte polynomials

Authors: D'Adderio, Michele and Moci, Luca

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted on: January 31, 2017
Keywords: arithmetic matroids, Gale duality, Tutte polynomial, toric arrangements,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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