A generalization of the Verlinde formula in logarithmic conformal field theory

We propose a generalized Verlinde formula associated with $(1,p)$ logarithmic models of two-dimensional conformal field theories, which have applications in statistical physics problems such as the sand-pile model and phase transitions in polymers. This formula gives the integer structure constants in the whole $(3p{-}1)$-dimensional space of vacuum torus amplitudes in which the fusion algebra is a $2p$-dimensional subalgebra.