On generic and maximal k-ranks of binary forms

Samuel Lundqvist, Alessandro Oneto, Bruce Reznick, Boris Shapiro

Research output: Contribution to journalArticlepeer-review


In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number of variables. The second one (by the fourth author) deals with the maximal k-rank of binary forms. We settle the first conjecture in the cases of two variables and the second in the first non-trivial case of the 3-rd powers of quadratic binary forms.

Original languageEnglish (US)
Pages (from-to)2062-2079
Number of pages18
JournalJournal of Pure and Applied Algebra
Issue number5
StatePublished - May 2019

ASJC Scopus subject areas

  • Algebra and Number Theory


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