An algorithm for computing plethysm coefficients

Yang, Mei

doi:10.1016/s0012-365x(97)00127-1

Cited by 11 publications

(5 citation statements)

References 2 publications

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“…While there are algorithms for computing a ν λ,µ (see for example [4,23]), no satisfying combinatorial description has been found. In this section we describe two rectangular symmetries satisfied by the plethysm coefficients.…”

Section: Plethysm Coefficientsmentioning

confidence: 99%

Rectangular Symmetries for Coefficients of Symmetric Functions

Briand

Orellana

Rosas

2015

Electron. J. Combin.

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Section: Plethysm Coefficientsmentioning

confidence: 99%

Rectangular Symmetries for Coefficients of Symmetric Functions

Briand

Orellana

Rosas

2015

Electron. J. Combin.

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“…We do not apply it directly, as it relies on 'nested inverse Kostka numbers'. As explained in [Yan98,Yan02], the computation of those, although possible in many cases, is a nontrivial task. For this reason, we introduce one more change of basis of symmetric polynomials, relating our results to transportation polytopes.…”

Section: Charactersmentioning

confidence: 99%

Plethysm and Lattice Point Counting

Kahle

Michałek

2015

Found Comput Math

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We apply lattice point counting methods to compute the multiplicities in the plethysm of 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 μ of 3, 4, or 5, we obtain an explicit formula in λ and k for the multiplicity of S λ in S μ (S k ).

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“…Numerous algorithms have been developed for computing the Schur expansion of a plethysm (most recently [5,6,25]), and several specific cases and extremal results have been obtained [2,3,4,15,22,26]. But an explicit combinatorial formula for the full Schur expansion of an arbitrary plethysm s λ [s μ ] has proved elusive.…”

Section: Introductionmentioning

confidence: 99%

Quasisymmetric expansions of Schur-function plethysms

Loehr

Warrington

2012

Proc. Amer. Math. Soc.

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Let s μ denote a Schur symmetric function and Q α a fundamental quasisymmetric function. Explicit combinatorial formulas are developed for the fundamental quasisymmetric expansions of the plethysms s μ [s ν ] and s μ [Q α ], as well as for related plethysms defined by inequality conditions. The key tools for obtaining these expansions are new standardization and reading word constructions for matrices.

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An algorithm for computing plethysm coefficients

Cited by 11 publications

References 2 publications

Rectangular Symmetries for Coefficients of Symmetric Functions

Rectangular Symmetries for Coefficients of Symmetric Functions

Plethysm and Lattice Point Counting

Quasisymmetric expansions of Schur-function plethysms

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