A note on the simultaneous Waring rank of monomials

Carlini, Enrico; Ventura, Emanuele

doi:10.1215/ijm/1534924838

Cited by 4 publications

(1 citation statement)

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“…Our approach to the problem is based on the study of simultaneous Waring decompositions of a collection of homogeneous polynomials. The problem of determining simultaneous ranks dates back to Terracini, see [Ter15]; some related problems were addressed more recently in [Fon02,AGMO18,CV18]. The simultaneous Waring rank of a collection of homogeneous polynomials is the minimum number of linear forms needed to simultaneously write a Waring decomposition for every polynomial in the collection.…”

Section: Introductionmentioning

confidence: 99%

Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank

Gesmundo¹,

Oneto²,

Ventura³

2019

SIAM J. Matrix Anal. Appl.

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A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. We show how the study of the simultaneous symmetric rank of partial derivatives of the homogeneous polynomial associated to the symmetric tensor can be used to prove equalities among different partially symmetric ranks. We apply this to the special cases of binary forms, ternary and quaternary cubics, monomials, and elementary symmetric polynomials.2010 Mathematics Subject Classification. (Primary) 15A69, 13P05 (Secondary) 13A02, 14N05.

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