The Jacobi factor of a plane curve singularity with one Puiseux pair admits an affine cell decomposition. J. Piontkowski showed that the cells are enumerated by the semigroup modules and gave a combinatorial formula for the dimension of such a cell. In a joint work with M. Mazin we relate these cells and their dimensions to the combinatorics of certain Young diagrams. The resulting partition statistics generalize the combinatorial constructions which appeared in the study of the bigraded deformation of Catalan numbers introduced by A. Garsia and M. Haiman.