Monomials as sums of kth-powers of forms

Enrico Carlini, Alessandro Oneto

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Motivated by recent results on the Waring problem for polynomial rings [4] and representation of monomial as sum of powers of linear forms [3], we consider the problem of presenting monomials of degree kd as sums of kth-powers of forms of degree d. We produce a general bound on the number of summands for any number of variables which we refine in the two variables case. We completely solve the k = 3 case for monomials in two and three variables.
Original languageEnglish
Pages (from-to)650-658
Number of pages9
JournalCommunications in Algebra
Issue number2
Publication statusPublished - 2015


  • Monomials
  • Sum of powers
  • Waring problems

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