Collectanea Mathematica

, Volume 67, Issue 3, pp 431–441 | Cite as

Some examples of forms of high rank



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 \({\ge }5\) these are the first examples showing that there exist forms with Waring rank strictly greater than the generic value.


Waring rank Apolarity Power sum decompositions 

Mathematics Subject Classification

Primary: 13P05 Secondary: 15A69 14N15 


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Copyright information

© Universitat de Barcelona 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics, Computer Science and MechanicsUniversity of WarsawWarsawPoland
  2. 2.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland
  3. 3.Department of MathematicsBoise State UniversityBoiseUSA

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