AN IMPROVED UPPER BOUND FOR THE WARING RANK OF THE DETERMINANT

被引：1

作者：

Johns, Garritt ^{[1
]}

Teitler, Zach ^{[1
]}

机构：

[1] Boise State Univ, Dept Math, Boise, ID 83725 USA

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2022年 / 14卷 / 03期

关键词：

Waring rank; symmetric rank; determinant;

D O I：

10.1216/jca.2022.14.415

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Waring rank of the generic d x d determinant is bounded above by d middot 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. We describe some of the symmetries of the decomposition and set-theoretic defining equations for the terms of the decomposition.

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收藏

页码：415 / 425

页数：11

相关论文

共 21 条

[1] Identifiability for a Class of Symmetric Tensors [J].

Angelini, Elena ;

Chiantini, Luca ;

Mazzon, Andrea .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2019, 16 (04)

[2] On polynomials with given Hilbert function and applications [J].

Bernardi, Alessandra ;

Jelisiejew, Joachim ;

Marques, Pedro Macias ;

Ranestad, Kristian .

COLLECTANEA MATHEMATICA, 2018, 69 (01) :39-64

[3] A bound for the Waring rank of the determinant via syzygies [J].

Boij, Mats ;

Teitler, Zach .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 587 :195-214

[4]

Conner A., 2021, EXP MATH, V30, P383

[5]

Conner A, 2019, Arxiv, DOI arXiv:1911.07981

[6] RANK AND BORDER RANK OF KRONECKER POWERS OF TENSORS AND STRASSEN'S LASER METHOD [J].

Conner, Austin ;

Gesmundo, Fulvio ;

Landsberg, Joseph M. ;

Ventura, Emanuele .

COMPUTATIONAL COMPLEXITY, 2022, 31 (01)

[7] On the Nuclear Norm and the Singular Value Decomposition of Tensors [J].

Derksen, Harm .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2016, 16 (03) :779-811

[8] Lower bound for ranks of invariant forms [J].

Derksen, Harm ;

Teitler, Zach .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (12) :5429-5441

[9]

Dolgachev IV, 2012, CLASSICAL ALGEBRAIC GEOMETRY: A MODERN VIEW, P1, DOI 10.1017/CBO9781139084437

[10]

Elencwajg G., 2011, ANSWER PARITY PERMUT