Poincaré series of a toric variety

For an affine toric variety X we compute the Poincaré series of the multi-index filtration defined by a finite number of monomial divisorial valuations on the ring OX,0. We give an alternative description of the Poincaré series as an integral with respect to the Euler characteristic over the projectivization of the space of germs OX,0. In particular we study divisorial valuations on the ring OCd,0 that arise by considering toric constellations. We give an explicit formula for the Poincaré series and a nice geometric description. This generalizes an expression of the Poincaré series for curves and rational surface singularities.