Waring Decompositions of Monomials

Weronika Buczyńska; Jarosław Buczyński; Zach Teitler

Waring Decompositions of Monomials

Weronika Buczyńska, Jarosław Buczyński, Zach Teitler

Mathematics Department

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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
Journal	Journal of Algebra
State	Published - 15 Mar 2013

Keywords

Waring decomposition
Waring rank
canonical forms
variety of sums of powers

EGS Disciplines

Mathematics

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Waring Decompositions of MonomialsFinal published version, 382 KBLicense: Unspecified

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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.",

keywords = "Waring decomposition, Waring rank, canonical forms, variety of sums of powers",

author = "Weronika Buczy{\'n}ska and Jaros{\l}aw Buczy{\'n}ski and Zach Teitler",

note = "Buczy{\'n}ska, Weronika; Buczy{\'n}ski, Jaros{\l}aw; and Teitler, Zach. (2013). {"}Waring Decompositions of Monomials{"}. Journal of Algebra, 378, 45-57. https://doi.org/10.1016/j.jalgebra.2012.12.011",

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T1 - Waring Decompositions of Monomials

AU - Buczyńska, Weronika

AU - Buczyński, Jarosław

AU - Teitler, Zach

N1 - Buczyńska, Weronika; Buczyński, Jarosław; and Teitler, Zach. (2013). "Waring Decompositions of Monomials". Journal of Algebra, 378, 45-57. https://doi.org/10.1016/j.jalgebra.2012.12.011

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 - Waring decomposition

KW - Waring rank

KW - canonical forms

KW - variety of sums of powers

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

M3 - Article

SN - 0021-8693

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Waring Decompositions of Monomials

Abstract

Keywords

EGS Disciplines

Access to Document

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