论文信息 - The solution to the Waring problem for monomials and the sum of coprime monomials

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

Abstract In this paper we compute the Waring rank of any polynomial of the form F = ∑ i = 1 r M i , where the M i are pairwise coprime monomials, i.e., GCD ( M i , M j ) = 1 for i ≠ 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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