Equality of symmetrized tensors and the flag variety

Berget, Andrew

doi:10.1016/j.laa.2011.03.036

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Theorem 83 (Dias Da Silva1

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Cited by 2 publications

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“…The following result is related to a generalization of Gamas's theorem on the vanishing of symmetrized tensors (see [3,13]). As an immediate corollary we have the following result.…”

Section: Theorem 83 (Dias Da Silvamentioning

confidence: 99%

Matrix orbit closures

Berget

Fink

2018

Beitr Algebra Geom

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Let G be the group GLr(C) × (C × ) n . We conjecture that the finely-graded Hilbert series of a G orbit closure in the space of r-by-n matrices is wholly determined by the associated matroid. In support of this, we prove that the coefficients of this Hilbert series corresponding to certain hook-shaped Schur functions in the GLr(C) variables are determined by the matroid, and that the orbit closure has a set-theoretic system of ideal generators whose combinatorics are also so determined. We also discuss relations between these Hilbert series for related matrices, including their stabilizing behaviour as r increases.

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“…The following result is related to a generalization of Gamas's theorem on the vanishing of symmetrized tensors (see [3,13]). As an immediate corollary we have the following result.…”

Section: Theorem 83 (Dias Da Silvamentioning

confidence: 99%

Matrix orbit closures

Berget

Fink

2018

Beitr Algebra Geom

Self Cite

View full text Add to dashboard Cite

show abstract

“…Landsberg, Jason Morton, and Sergey Norin are about a promising new area in theoretical computer science called holographic algorithms [30], the main tenet of which is a scheme to solve difficult enumeration problems via clever tensor contractions. Another article with a similar combinatorial flavor is [3] by Andrew Berget, which contains a new short proof of a result due to Chollet and Marcus [9].…”

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confidence: 99%