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Arithmetic matroids, the Tutte polynomial and toric arrangements

Authors
  • D’Adderio, Michele
  • Moci, Luca
Type
Published Article
Journal
Advances in Mathematics
Publication Date
Jan 01, 2012
Accepted Date
Sep 02, 2012
Volume
232
Issue
1
Pages
335–367
Identifiers
DOI: 10.1016/j.aim.2012.09.001
Source
Elsevier
Keywords
License
Unknown

Abstract

We introduce the notion of an arithmetic matroid whose main example is 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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