Combinatorial generators for the cohomology of toric arrangements

We give a new combinatorial description of the cohomology ring structure of $H^{\ast }(M(\mathcal{A});\mathbb{Z})$ of the complement $M(\mathcal{A})$ of a real complexified toric arrangement $\mathcal{A}$ in $({\mathbb{C}}^{\ast }{)}^d$. In particular, we correct an error in the paper ``The integer cohomology algebra of toric arrangements’', Adv. Math., 2017.