Maximum Waring Ranks of Monomials and Sums of Coprime Monomials

Erik Holmes; Paul Plummer; Jeremy Siegert; Zach Teitler

doi:10.1080/00927872.2015.1087534

Maximum Waring Ranks of Monomials and Sums of Coprime Monomials

Erik Holmes
, Paul Plummer
, Jeremy Siegert
, Zach Teitler

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

1 Scopus citations

Abstract

We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.

Original language	English
Pages (from-to)	4212-4219
Number of pages	8
Journal	Communications in Algebra
Volume	44
Issue number	10
DOIs	https://doi.org/10.1080/00927872.2015.1087534
State	Published - 2 Oct 2016
Externally published	Yes

Keywords

Maximum Waring rank
Upper bounds for Waring rank
Waring problem for homogeneous polynomials
Waring rank

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2015.1087534

Cite this

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title = "Maximum Waring Ranks of Monomials and Sums of Coprime Monomials",

abstract = "We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.",

keywords = "Maximum Waring rank, Upper bounds for Waring rank, Waring problem for homogeneous polynomials, Waring rank",

author = "Erik Holmes and Paul Plummer and Jeremy Siegert and Zach Teitler",

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AU - Holmes, Erik

AU - Plummer, Paul

AU - Siegert, Jeremy

AU - Teitler, Zach

PY - 2016/10/2

Y1 - 2016/10/2

N2 - We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.

AB - We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.

KW - Maximum Waring rank

KW - Upper bounds for Waring rank

KW - Waring problem for homogeneous polynomials

KW - Waring rank

UR - https://www.scopus.com/pages/publications/84976254528

U2 - 10.1080/00927872.2015.1087534

DO - 10.1080/00927872.2015.1087534

M3 - Article

AN - SCOPUS:84976254528

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VL - 44

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -

Maximum Waring Ranks of Monomials and Sums of Coprime Monomials

Abstract

Keywords

ASJC Scopus subject areas

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