Foundations of Computational Mathematics

, Volume 16, Issue 5, pp 1241–1261

Plethysm and Lattice Point Counting

Article

DOI: 10.1007/s10208-015-9275-7

Cite this article as:
Kahle, T. & Michałek, M. Found Comput Math (2016) 16: 1241. doi:10.1007/s10208-015-9275-7

Abstract

We apply lattice point counting methods to compute the multiplicities in the plethysm of \(\textit{GL}(n)\). Our approach gives insight into the asymptotic growth of the plethysm and makes the problem amenable to computer algebra. We prove an old conjecture of Howe on the leading term of plethysm. For any partition \(\mu \) of 3, 4, or 5, we obtain an explicit formula in \(\lambda \) and k for the multiplicity of \(S^\lambda \) in \(S^\mu (S^k)\).

Keywords

PlethysmEhrhart functionQuasi-polynomialLattice point counting

Mathematics Subject Classification

Primary: 20G0511P21Secondary: 11H0605A1652B2052B5520C15

Copyright information

© SFoCM 2015

Authors and Affiliations

  1. 1.Fakultät für MathematikOtto-von-Guericke UniversitätMagdeburgGermany
  2. 2.Polish Academy of SciencesWarsawPoland
  3. 3.Simons Institute for the Theory of ComputingUC BerkeleyBerkeleyUSA