Lenz, Matthias 2019 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. application/pdf https://folia.unifr.ch/global/documents/308122 https://folia.unifr.ch/documents/308122/files/len_rwm.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00026-019-00424-z info:eu-repo/semantics/openAccess License undefined Annals of Combinatorics. - 2019, vol. 23, no. 2, p. 335–346 info:eu-repo/classification/udc/51 Representations of weakly multiplicative arithmetic matroids are unique http://purl.org/coar/resource_type/c_6501