The solution to the Waring problem for monomials and the sum of coprime monomials

JOURNAL OF ALGEBRA

卷:370

Article

Carlini, Enrico¹  Catalisano, Maria Virginia²  Geramita, Anthony V.^3,4 

[1] Politecn Torino, Dipartimento Sci Matemat, Turin, Italy

[2] Univ Genoa, Dipartimento Ingn Meccan Energet Prod Trasporti &, Genoa, Italy

[3] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

[4] Univ Genoa, Dipartimento Matemat, Genoa, Italy

关键词: Waring problem for homogeneous polynomial;    Waring rank;   

DOI  :  10.1016/j.jalgebra.2012.07.028

来源: Elsevier

【 摘 要 】

In this paper we compute the Waring rank of any polynomial of the form F = Sigma(r)(i=1) M-i, where the M-i are pairwise coprime monomials, i.e., GCD(M-i, M-j) = 1 for i not equal j. In particular, we determine the Waring rank of any monomial. As an application we show that certain monomials in three variables give examples of forms of rank higher than the generic form. As a further application we produce a sum of power decomposition for any form which is the sum of pairwise coprime monomials. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free