Progress on the symmetric Strassen conjecture

被引：15

作者：

Carlini, Enrico ^{[1
,2
]}

Catalisano, Maria Virginia ^{[3
]}

Chiantini, Luca ^{[4
]}

机构：

[1] Politecn Torino, Dept Math Sci, Turin, Italy

[2] Monash Univ, Sch Math Sci, Clayton, Vic, Australia

[3] Univ Genoa, DIME Dipartimento Ingn Meccan Energet Gestionale, I-16126 Genoa, Italy

[4] Univ Siena, Dept Informat Engn & Math, I-53100 Siena, Italy

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2015年 / 219卷 / 08期

关键词：

MATRIX MULTIPLICATION; SUM;

D O I：

10.1016/j.jpaa.2014.10.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F and G be homogeneous polynomials in disjoint sets of variables. We prove that the Waring rank is additive, thus proving the symmetric Strassen conjecture, when either F or G is a power, or F and G have two variables, or either F or G has small rank. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：3149 / 3157

页数：9

共 17 条

[1] Alexander James, 1995, J. Algebraic Geom., V4, P201
[2] Decomposition of homogeneous polynomials with low rank
Ballico, Edoardo
Bernardi, Alessandra
[J]. MATHEMATISCHE ZEITSCHRIFT, 2012, 271 (3-4) : 1141 - 1149
[3] GEOMETRIC CONSEQUENCES OF EXTREMAL BEHAVIOR IN A THEOREM OF MACAULAY
BIGATTI, A
GERAMITA, AV
MIGLIORE, JC
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 346 (01) : 203 - 235
[4] Reducing the number of variables of a polynomial
Carlini, Enrico
[J]. ALGEBRAIC GEOMETRY AND GEOMETRIC MODELING, 2006, : 237 - 247
[5] The solution to the Waring problem for monomials and the sum of coprime monomials
Carlini, Enrico
Catalisano, Maria Virginia
Geramita, Anthony V.
[J]. JOURNAL OF ALGEBRA, 2012, 370 : 5 - 14
[6] 3-dimensional sundials
Carlini, Enrico
Catalisano, Maria Virginia
Geramita, Anthony V.
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2011, 9 (05): : 949 - 971
[7] On the Rank of a Binary Form
Comas, Gonzalo
Seiguer, Malena
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2011, 11 (01) : 65 - 78
[8] Eisenbud D., 1995, GRAD TEXTS MATH, V150
[9] ON THE DIRECT SUM CONJECTURE
FEIG, E
WINOGRAD, S
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 63 (DEC) : 193 - 219
[10] Geramita A., 1996, QUEENS PAPERS PURE A, V102, P2

← 1 2 →