A Bound for the Waring Rank of the Determinant via Syzygies

Mats Boij; Zach Teitler

doi:10.1016/j.laa.2019.11.007

A Bound for the Waring Rank of the Determinant via Syzygies

Mats Boij
, Zach Teitler

Mathematics Department

KTH Royal Institute of Technology

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

4 Scopus citations

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Abstract

We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.

Original language	American English
Pages (from-to)	195-214
Number of pages	20
Journal	Linear Algebra and Its Applications
Volume	587
DOIs	https://doi.org/10.1016/j.laa.2019.11.007
State	Published - 15 Feb 2020

Keywords

Determinants
Permanents
Symmetric cactus rank
Symmetric rank
Syzygies
Waring rank

EGS Disciplines

Mathematics

Access to Document

10.1016/j.laa.2019.11.007

A Bound for the Waring Rank of the Determinant via SyzygiesAccepted author manuscript, 561 KBLicense: CC BY-NC-ND

Cite this

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title = "A Bound for the Waring Rank of the Determinant via Syzygies",

abstract = "We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.",

keywords = "Determinants, Permanents, Symmetric cactus rank, Symmetric rank, Syzygies, Waring rank",

author = "Mats Boij and Zach Teitler",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.laa.2019.11.007",

language = "American English",

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AU - Teitler, Zach

PY - 2020/2/15

Y1 - 2020/2/15

N2 - We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.

AB - We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.

KW - Determinants

KW - Permanents

KW - Symmetric cactus rank

KW - Symmetric rank

KW - Syzygies

KW - Waring rank

UR - https://www.scopus.com/pages/publications/85074761605

UR - https://scholarworks.boisestate.edu/math_facpubs/233

U2 - 10.1016/j.laa.2019.11.007

DO - 10.1016/j.laa.2019.11.007

M3 - Article

SN - 0024-3795

VL - 587

SP - 195

EP - 214

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A Bound for the Waring Rank of the Determinant via Syzygies

Abstract

Keywords

EGS Disciplines

Access to Document

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