Foundations of Computational Mathematics

, Volume 16, Issue 5, pp 1241–1261 | Cite as

Plethysm and Lattice Point Counting

Article

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

Plethysm Ehrhart function Quasi-polynomial Lattice point counting 

Mathematics Subject Classification

Primary: 20G05 11P21 Secondary: 11H06 05A16 52B20 52B55 20C15 

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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

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