In this paper we compute the Waring rank of any polynomial of the form F=M1+...+Mr, where the Mi are pairwise coprime monomials, i.e., GCD(Mi, Mj)=1 for i different from 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.
The solution to the Waring problem for monomials and the sum of coprime monomials
CATALISANO, MARIA VIRGINIA;GERAMITA, ANTHONY VITO
2012-01-01
Abstract
In this paper we compute the Waring rank of any polynomial of the form F=M1+...+Mr, where the Mi are pairwise coprime monomials, i.e., GCD(Mi, Mj)=1 for i different from 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.
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