Some examples of forms of high rank

Jarosław Buczyński, Zach Teitler

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We describe some forms with greater Waring rank than previous examples. In 3 variables we give forms of odd degree with strictly greater rank than the ranks of monomials, the previously highest known rank. This narrows the possible range of values of the maximum Waring rank of forms in 3 variables. In 4 variables we give forms of odd degree with strictly greater than generic rank. In degrees ≥ 5 these are the first examples showing that there exist forms with Waring rank strictly greater than the generic value.

Original languageEnglish
Pages (from-to)431-441
Number of pages11
JournalCollectanea Mathematica
Volume67
Issue number3
DOIs
StatePublished - 1 Sep 2016

Keywords

  • Apolarity
  • Power sum decompositions
  • Waring rank

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