Representations of weakly multiplicative arithmetic matroids are unique

Lenz, Matthias

doi:10.1007/s00026-019-00424-z

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Journal article

Representations of weakly multiplicative arithmetic matroids are unique

Lenz, Matthias Département de Mathématiques, Université de Fribourg, Switzerland

2019

Published in:

Annals of Combinatorics. - 2019, vol. 23, no. 2, p. 335–346

English An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such an arithmetic matroid can be represented by an integer matrix, then this matrix is uniquely determined. This implies that the integral cohomology ring of a centered toric arrangement whose arithmetic matroid is weakly multiplicative is determined by its poset of layers. This partially answers a question asked by Callegaro–Delucchi.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language