A proof of the set-theoretic version of the salmon conjecture

被引：17
|
作者：
Friedland, Shmuel [1 ]
Gross, Elizabeth [1 ]
机构：
[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
来源：
JOURNAL OF ALGEBRA | 2012年 / 356卷 / 01期
关键词：
Rank of tensors; Border rank of tensors; Salmon conjecture; SECANT VARIETIES;
D O I：
10.1016/j.jalgebra.2012.01.017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the irreducible variety of 4 x 4 x 4 complex valued tensors of border rank at most 4 is the zero set of polynomial equations of degree 5 (the Strassen commutative conditions), of degree 6 (the Landsberg-Manivel polynomials), and of degree 9 (the symmetrization conditions). (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：374 / 379
页数：6
相关论文
共 50 条
  • [31] SET-THEORETIC ANALYSIS OF PERIODIC RECTIFICATION
    KIVA, VN
    SERAFIMOV, LA
    ZHURNAL FIZICHESKOI KHIMII, 1976, 50 (01): : 54 - 57
  • [32] The Buddhist conditional in set-theoretic terms
    Galloway, B
    JOURNAL OF INDIAN PHILOSOPHY, 1996, 24 (06) : 649 - 658
  • [33] Set-theoretic pluralism and the Benacerraf problem
    Justin Clarke-Doane
    Philosophical Studies, 2020, 177 : 2013 - 2030
  • [34] Combining algebraic and set-theoretic specifications
    Hintermeier, C
    Kirchner, H
    Mosses, PD
    RECENT TRENDS IN DATA TYPE SPECIFICATION, 1996, 1130 : 255 - 273
  • [35] Set-Theoretic Types for Polymorphic Variants
    Castagna, Giuseppe
    Petrucciani, Tommaso
    Nguyen, Kim
    ACM SIGPLAN NOTICES, 2016, 51 (09) : 378 - 391
  • [36] THE SOUSLIN NUMBER IN SET-THEORETIC TOPOLOGY
    SHAPIROVSKII, BE
    TOPOLOGY AND ITS APPLICATIONS, 1994, 57 (2-3) : 131 - 150
  • [37] Set-theoretic Analysis of Nominative Data
    Skobelev, Volodymyr G.
    Ivanov, Ievgen
    Nikitchenko, Mykola
    COMPUTER SCIENCE JOURNAL OF MOLDOVA, 2015, 23 (03) : 270 - 288
  • [38] Set-Theoretic Solutions of the Pentagon Equation
    Colazzo, Ilaria
    Jespers, Eric
    Kubat, Lukasz
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 380 (02) : 1003 - 1024
  • [39] A SET-THEORETIC APPROACH TO MIMO DETECTION
    Fink, Jochen
    Cavalcante, Renato L. G.
    Utkovski, Zoran
    Stanczak, Slawomir
    2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2022, : 5328 - 5332
  • [40] A set-theoretic approach to organizational configurations
    Fiss, Peer C.
    ACADEMY OF MANAGEMENT REVIEW, 2007, 32 (04): : 1180 - 1198
12345