Database of Piecewise Quasipolynomial Functions

A quasipolynomial is a function on integer points given by several polynomials: one for each coset of some full-rank sublattice. The piecewise quasipolynomial functions considered here have as domains of quasipolynomiality the maximal cells of a fan subdividing a cone, and are zero outside this cone. This database provides a full description of some small multiplicity functions from representation theory that are piecewise quasipolynomial in this sense. This includes or will include families of Littlewood-Richardson coefficients, Kronecker coefficients, Plethysm coefficients and alike. Each data is provided as a JSON file. SageMath Jupyter Notebooks provide examples of use of the data. Sagemath code is provided to import the data in Sagemath. This work is supported by Grant PID2020-117843GB-I00 funded by MICIU/AEI/10.13039/501100011033