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

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Abstract

In this paper we compute the Waring rank of any polynomial of the form F=∑i=1rMi, 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. © 2012 Elsevier Inc.

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Carlini, E., Catalisano, M. V., & Geramita, A. V. (2012). The solution to the Waring problem for monomials and the sum of coprime monomials. Journal of Algebra, 370, 5–14. https://doi.org/10.1016/j.jalgebra.2012.07.028

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