Relation between the Hilbert series of quadratic dual algebras does not imply the Koszul property (Q1916680)

Let \(A\) be a quadratic algebra. The author shows that Fröberg's formula does not imply in general that \(A\) is a Koszul algebra. The counterexample is realized as a Segre tensor product. It is also shown that the double Poincaré series \(P_A(s,t)\) does not determine the Poincaré series \(P_{A^!}(s,t)\) of the dual algebra \(A^!\).