English

On the typical rank of real binary forms

Algebraic Geometry 2009-09-29 v1 Statistics Theory Statistics Theory

Abstract

We determine the rank of a general real binary form of degree d=4 and d=5. In the case d=5, the possible values of the rank of such general forms are 3,4,5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.

Keywords

Cite

@article{arxiv.0909.4865,
  title  = {On the typical rank of real binary forms},
  author = {Pierre Comon and Giorgio Ottaviani},
  journal= {arXiv preprint arXiv:0909.4865},
  year   = {2009}
}

Comments

12 pages, 2 figures

R2 v1 2026-06-21T13:50:55.908Z