Title: Representations of weakly multiplicative arithmetic matroids are unique,
Abstract: 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
integer cohomology ring of a centred toric arrangement whose arithmetic matroid
is weakly multiplicative is determined by its poset of layers. This partially
answers a question asked by Callegaro-Delucchi.