On the Waring problem for polynomial rings

DOI10.1073/pnas.1120984109zbMath1302.11077arXiv1112.1371OpenAlexW2065364146WikidataQ35889401 ScholiaQ35889401MaRDI QIDQ4907488

Ralf Fröberg, Boris Zalmanovich Shapiro, Giorgio Ottaviani

Publication date: 2 February 2013

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.1371

zbMATH Keywords

Veronese embeddingWaring problemsums of powers of homogeneous polynomials

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Arithmetic theory of polynomial rings over finite fields (11T55)

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Lower Bounds for Sums of Powers of Low Degree Univariates ⋮ Sum of squares length of real forms ⋮ A case of multivariate Birkhoff interpolation using high order derivatives ⋮ Identifiability for mixtures of centered Gaussians and sums of powers of quadratics ⋮ On the degree of varieties of sum of squares ⋮ Zero-dimensional complete intersections and their linear span in the Veronese embeddings of projective spaces ⋮ Waring identifiability for powers of forms via degenerations ⋮ The monic rank ⋮ Waring rank of symmetric tensors, and singularities of some projective hypersurfaces ⋮ On generic and maximal \(k\)-ranks of binary forms ⋮ On maximum, typical and generic ranks ⋮ Algebraic stories from one and from the other pockets ⋮ Efficient Evaluation of Noncommutative Polynomials Using Tensor and Noncommutative Waring Decompositions ⋮ Monomials as Sums ofk th-Powers of Forms ⋮ Waring rank of binary forms, harmonic cross-ratio and golden ratio ⋮ The Hitchhiker guide to: secant varieties and tensor decomposition ⋮ On a class of power ideals

Cites Work

• Secant varieties to osculating varieties of Veronese embeddings of \(\mathbb P^n\)
• Inverse system of a symbolic power. II: The Waring problem for forms
• The strict Waring problem for polynomial rings
• On the Alexander-Hirschowitz theorem
• Combinatorics and geometry of power ideals
• An inequality for Hilbert series of graded algebras.
• Trees, parking functions, syzygies, and deformations of monomial ideals

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