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Correlators in topological theories are given by the values of a linear formon the products of operators from a commutative associative algebra (CAA). As acorollary, partition functions of topological theory always satisfy thegeneralized WDVV equations. We consider the Hurwitz partition functions,associated in this way with the CAA of cut-and-join operators. The ordinaryHurwitz numbers for a given number of sheets in the covering provide trivial(sums of exponentials) solutions to the WDVV equations, with finite number oftime-variables. The generalized Hurwitz numbers from arXiv:0904.4227 provide anon-trivial solution with infinite number of times. The simplest solution ofthis type is associated with a subring, generated by the dilatation operatorstr X(d/dX).

Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations