On generic and maximal \(k\)-ranks of binary forms

DOI10.1016/j.jpaa.2018.08.015zbMath1409.15013arXiv1711.05014OpenAlexW2769169516WikidataQ129359307 ScholiaQ129359307MaRDI QIDQ1713025

Alessandro Oneto, Bruce Reznick, Samuel Lundqvist, Boris Zalmanovich Shapiro

Publication date: 24 January 2019

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.05014

zbMATH Keywords

binary formrankhomogeneous polynomialWaring decomposition

Mathematics Subject Classification ID

Quadratic and bilinear forms, inner products (15A63) Multilinear algebra, tensor calculus (15A69) Canonical forms, reductions, classification (15A21) Classical problems, Schubert calculus (14N15) General binary quadratic forms (11E16)

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Uses Software

• Macaulay2

Cites Work

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• The Pythagoras number of real sum of squares polynomials and sum of square magnitudes of polynomials
• Eigenvectors of tensors and algorithms for Waring decomposition
• Some new canonical forms for polynomials
• A note on Fröberg's conjecture for forms of equal degrees
• Symmetric tensor decomposition
• Computing symmetric rank for symmetric tensors
• On the rank of a binary form
• Thin algebras of embedding dimension three
• On Hilbert series for commutative and noncommutative graded algebras
• Hilbert functions of graded algebras
• The Veronese variety and catalecticant matrices
• Fat points, inverse systems, and piecewise polynomial functions
• On maximum, typical and generic ranks
• On the X-rank with respect to linear projections of projective varieties
• An inequality for Hilbert series of graded algebras.
• On the Waring problem for polynomial rings
• On the Hilbert series of ideals generated by generic forms
• Monomials as Sums ofk th-Powers of Forms
• On the Length of Binary Forms

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