Waring Decompositions of Monomials

Weronika Buczyńska; Jarosław Buczyński; Zach Teitler

doi:10.1016/j.jalgebra.2012.12.011

Waring Decompositions of Monomials

Weronika Buczyńska
, Jarosław Buczyński
, Zach Teitler

Mathematics Department

Université Grenoble
Institute of Mathematics of the Polish Academy of Sciences

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

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Abstract

A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables.

Original language	American English
Pages (from-to)	45-57
Number of pages	13
Journal	Journal of Algebra
Volume	378
DOIs	https://doi.org/10.1016/j.jalgebra.2012.12.011
State	Published - 15 Mar 2013

Keywords

Canonical forms
Variety of sums of powers
Waring decomposition
Waring rank

EGS Disciplines

Mathematics

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10.1016/j.jalgebra.2012.12.011

Waring Decompositions of MonomialsFinal published version, 382 KBLicense: Unspecified

Cite this

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title = "Waring Decompositions of Monomials",

abstract = "A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables.",

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T1 - Waring Decompositions of Monomials

AU - Buczyńska, Weronika

AU - Buczyński, Jarosław

AU - Teitler, Zach

PY - 2013/3/15

Y1 - 2013/3/15

N2 - A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables.

AB - A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables.

KW - Canonical forms

KW - Variety of sums of powers

KW - Waring decomposition

KW - Waring rank

UR - https://www.scopus.com/pages/publications/84872345217

UR - https://scholarworks.boisestate.edu/math_facpubs/108

U2 - 10.1016/j.jalgebra.2012.12.011

DO - 10.1016/j.jalgebra.2012.12.011

M3 - Article

SN - 0021-8693

VL - 378

SP - 45

EP - 57

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Waring Decompositions of Monomials

Abstract

Keywords

EGS Disciplines

Access to Document

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