AN IMPROVED UPPER BOUND FOR THE WARING RANK OF THE DETERMINANT

Garritt Johns; Zach Teitler

doi:10.1216/jca.2022.14.415

AN IMPROVED UPPER BOUND FOR THE WARING RANK OF THE DETERMINANT

Garritt Johns, Zach Teitler

Mathematics Department

Boise State University

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

3 Scopus citations

Abstract

The Waring rank of the generic d ×d determinant is bounded above by d · d!. This improves previous upper bounds, which were of the form an exponential times the factorial. Our upper bound comes from an explicit power sum decomposition.

Original language	English
Pages (from-to)	415-425
Number of pages	11
Journal	Journal of Commutative Algebra
Volume	14
Issue number	3
DOIs	https://doi.org/10.1216/jca.2022.14.415
State	Published - Sep 2022

Keywords

Determinant
Symmetric rank
Waring rank

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10.1216/jca.2022.14.415

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title = "AN IMPROVED UPPER BOUND FOR THE WARING RANK OF THE DETERMINANT",

abstract = "The Waring rank of the generic d ×d determinant is bounded above by d · d!. This improves previous upper bounds, which were of the form an exponential times the factorial. Our upper bound comes from an explicit power sum decomposition.",

keywords = "Determinant, Symmetric rank, Waring rank",

author = "Garritt Johns and Zach Teitler",

note = "Publisher Copyright: {\textcopyright} Rocky Mountain Mathematics Consortium",

year = "2022",

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doi = "10.1216/jca.2022.14.415",

language = "English",

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AU - Teitler, Zach

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N2 - The Waring rank of the generic d ×d determinant is bounded above by d · d!. This improves previous upper bounds, which were of the form an exponential times the factorial. Our upper bound comes from an explicit power sum decomposition.

AB - The Waring rank of the generic d ×d determinant is bounded above by d · d!. This improves previous upper bounds, which were of the form an exponential times the factorial. Our upper bound comes from an explicit power sum decomposition.

KW - Determinant

KW - Symmetric rank

KW - Waring rank

UR - https://www.scopus.com/pages/publications/85141255392

U2 - 10.1216/jca.2022.14.415

DO - 10.1216/jca.2022.14.415

M3 - Article

AN - SCOPUS:85141255392

SN - 1939-0807

VL - 14

SP - 415

EP - 425

JO - Journal of Commutative Algebra

JF - Journal of Commutative Algebra

IS - 3

ER -

AN IMPROVED UPPER BOUND FOR THE WARING RANK OF THE DETERMINANT

Abstract

Keywords

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