The Waring rank of the sum of pairwise coprime monomials

2011/12/15 by Carlini, Enrico, Catalisano, Maria Virginia, Geramita, Anthony V.
#13P05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1112.3474

Abstract

In this paper we compute the Waring rank of any polynomial of the form F=M₁+...+M_r, where the M_i are pairwise coprime monomials, i.e., GCD(M_i,M_j)=1 for i not 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.

Related

• Maximum Waring ranks of monomials
• The Solution to Waring's Problem for Monomials
• A note on the simultaneous Waring rank of monomials
• Some examples of forms of high rank
• An upper bound for the Waring rank of a form