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.

引用

页码：415 / 425

页数：11

共 50 条

[1] A bound for the Waring rank of the determinant via syzygies
Boij, Mats
Teitler, Zach
LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 587 : 195 - 214
[2] An upper bound for the Waring rank of a form
Joachim Jelisiejew
Archiv der Mathematik, 2014, 102 : 329 - 336
[3] An upper bound for the Waring rank of a form
Jelisiejew, Joachim
ARCHIV DER MATHEMATIK, 2014, 102 (04) : 329 - 336
[4] A New Bound for the Waring Rank of Monomials\ast
Han, Kangjin
Moon, Hyunsuk
SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2022, 6 (03) : 407 - 431
[5] AN IMPROVED UPPER BOUND FOR G(K) IN WARING PROBLEM FOR RELATIVELY SMALL K
BALASUBRAMANIAN, R
MOZZOCHI, CJ
ACTA ARITHMETICA, 1984, 43 (03) : 283 - 285
[6] An upper bound for nonnegative rank
Shitov, Yaroslav
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2014, 122 : 126 - 132
[7] An upper bound for the minimum rank of a graph
Berman, Avi
Friedland, Shmuel
Hogben, Leslie
Rothblum, Uriel G.
Shader, Bryan
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (07) : 1629 - 1638
[8] On the waring rank of binary forms
Tokcan, Neriman
LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 524 : 250 - 262
[9] An Improved Upper Bound for SAT
Chu, Huairui
Xiao, Mingyu
Zhang, Zhe
THIRTY-FIFTH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE, THIRTY-THIRD CONFERENCE ON INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE AND THE ELEVENTH SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE, 2021, 35 : 3707 - 3714
[10] An improved upper bound for SAT
Dantsin, E
Wolpert, A
THEORY AND APPLICATIONS OF SATISFIABILITY TESTING, PROCEEDINGS, 2005, 3569 : 400 - 407

← 1 2 3 4 5 →