Progress on the symmetric Strassen conjecture

Carlini, Enrico Maria; Catalisano, Maria Virginia; Chiantini, Luca

doi:10.48550/arxiv.1405.3721

Cited by 3 publications

(3 citation statements)

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“…Another approach to lower bounds for Waring rank itself comes from the technique used to find Waring ranks of monomials and sums of pairwise coprime monomials in [CCG12]. Very recently this method has been developed further in [CCC14] and [Woo14]. So far it has been used to find Waring ranks of increasingly general examples, namely, sums of polynomials in small numbers of linearly independent variables.…”

Section: Classical Waring Rankmentioning

confidence: 99%

Geometric lower bounds for generalized ranks

Teitler

2014

Preprint

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We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of [LT10] and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the "non-Abelian" catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially symmetric tensors); a special case is the simultaneous Waring decomposition problem for a linear system of polynomials. We generalize the classical Apolarity Lemma to multihomogeneous polynomials and give some more general statements. Finally we revisit the lower bound of [RS11], and again generalize it to multihomogeneous polynomials and some more general settings.

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Section: Classical Waring Rankmentioning

confidence: 99%

Geometric lower bounds for generalized ranks

Teitler

2014

Preprint

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“…We thank Jarek Buczyński for suggesting this example and a proof that involved tensor rank. Since then, however, we have learned of a much quicker, elementary proof using a very recent result of Carlini, Catalisano, and Chiantini [CCC14]. They showed that r(F (x 1 , .…”

Section: Non-monomial Examplesmentioning

confidence: 99%