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≠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 / Carlini, Enrico; M., Catalisano; A., Geramita. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 370:1-2(2012), pp. 5-14. [10.1016/j.jalgebra.2012.07.028]

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

CARLINI, ENRICO;
2012

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≠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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2503658
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