A bound for the Waring rank of the determinant via syzygies

被引：4

作者：

Boij, Mats ^{[1
]}

Teitler, Zach ^{[2
]}

机构：

[1] KTH Royal Inst Technol, SE-10044 Stockholm, Sweden

[2] Boise State Univ, Dept Math, 1910 Univ Dr, Boise, ID 83725 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 587卷

基金：

瑞典研究理事会;

关键词：

Waring rank; Symmetric rank; Symmetric cactus rank; Determinants; Permanents; Syzygies; POWER SUM DECOMPOSITIONS; APOLARITY; EQUATIONS;

D O I：

10.1016/j.laa.2019.11.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the Waring rank of the 3 x 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 x 3 permanent is at least 14. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：195 / 214

页数：20

共 50 条

[1]

Alexander J., 1995, J. Algebraic Geom., V4, P201

[2] Syzygies of the apolar ideals of the determinant and permanent [J].