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Foundations of Computational Mathematics
Erschienen in: Foundations of Computational Mathematics 5/2016

01.10.2016

Plethysm and Lattice Point Counting

verfasst von: Thomas Kahle, Mateusz Michałek

Erschienen in: Foundations of Computational Mathematics | Ausgabe 5/2016

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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 \(S^\mu (S^k)\).
Vorheriger Artikel Sampling and Cubature on Sparse Grids Based on a B-spline Quasi-Interpolation
Nächster Artikel Generalized Sampling and Infinite-Dimensional Compressed Sensing

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Metadaten
Titel
Plethysm and Lattice Point Counting
verfasst von
Thomas Kahle
Mateusz Michałek
Publikationsdatum
01.10.2016
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 5/2016
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-015-9275-7

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