Annals of Combinatorics

, Volume 23, Issue 2, pp 335–346 | Cite as

Representations of Weakly Multiplicative Arithmetic Matroids are Unique

  • Matthias LenzEmail author


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.


Arithmetic matroid Representation Toric arrangement Combinatorial topology 

Mathematics Subject Classification

Primary 05B35 52C35 Secondary 14M15 14N20 57N65 



The author would like to thank Elia Saini for several interesting discussions and an anonymous referee for many helpful suggestions.


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Authors and Affiliations

  1. 1.Département de MathématiquesUniversité de FribourgFribourgSwitzerland

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