FoCM 2014 conference

Workshop C1 - Computational Algebraic Geometry

December 18, 18:30 ~ 18:50 - Room B12

Plethysm and lattice point counting

Thomas Kahle

Otto-von-Guericke Universität Magdeburg, Germany   -

We show that the coefficient of the Schur functor $S^\lambda$ in the decomposition of the plethysm $S^\mu(S^k)$ into irreducibles is the solution to a lattice point counting problem. Consequently, for each fixed $\mu$, the solution to this problem is a piecewise quasi-polynomial in $(\lambda,k)$. We show how to use computer algebra to determine this function explicitly when $\mu$ is a partition of 4 or 5. We also discuss asymptotics of the resulting piecewise quasi-polynomials.

Joint work with Mateusz Michalek (Simons Institute, UC Berkeley).

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