Waring decompositions of monomials

被引：26

作者：

Buczynska, Weronika ^{[1
]}

Buczynski, Jaroslaw ^{[1
,2
]}

Teitler, Zach ^{[3
]}

机构：

[1] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

[2] Univ Grenoble 1, Inst Fourier, F-38402 St Martin Dheres, France

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

来源：

JOURNAL OF ALGEBRA | 2013年 / 378卷

关键词：

Canonical forms; Waring rank; Waring decomposition; Variety of sums of powers; VARIETIES; POWERS; SUMS;

D O I：

10.1016/j.jalgebra.2012.12.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：45 / 57

页数：13

共 15 条

[1] [Anonymous], GRAD TEXTS MATH
[2] 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
[3] On the Rank of a Binary Form
Comas, Gonzalo
Seiguer, Malena
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2011, 11 (01) : 65 - 78
[4] Iarrobino A., 1999, Power sums, Gorenstein algebras, and determinantal loci, volume 1721 of Lecture Notes in Mathematics, V1721
[5] K3 surfaces of genus 8 and varieties of sums of powers of cubic fourfolds
Iliev, A
Ranestad, K
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (04) : 1455 - 1468
[6] Landsberg J., 2011, GRAD STUD MATH, V128
[7] On the Ranks and Border Ranks of Symmetric Tensors
Landsberg, J. M.
Teitler, Zach
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2010, 10 (03) : 339 - 366
[8] Mella M, 2009, P AM MATH SOC, V137, P91
[9] Mukai S., 1992, London Math. Soc., V179, P255
[10] Polynomials in several variables
Oldenburger, R
[J]. ANNALS OF MATHEMATICS, 1940, 41 : 694 - 710

← 1 2 →