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2011

Arithmetic matroids, Tutte polynomial, and toric arrangements

D'Adderio, Michele, Moci, Luca

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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.

Arithmetic matroids, Tutte polynomial, and toric arrangements · Around

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W. T. Tutte
1954
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H. Crapo
1969
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G. -C. Rota
1971
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A. P. Heron
1972
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J.H. Mason
1972
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D. Welsh
1976
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