On generic and maximal $k$-ranks of binary forms - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2017

On generic and maximal $k$-ranks of binary forms


In what follows, we pose two general conjectures about decompositions of homogeneous poly-nomials 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.
Fichier principal
Vignette du fichier
171113_LORS_arXiv.pdf (386.82 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01637944 , version 1 (18-11-2017)


  • HAL Id : hal-01637944 , version 1


Samuel Lundqvist, Alessandro Oneto, Bruce Reznick, Boris Shapiro. On generic and maximal $k$-ranks of binary forms. 2017. ⟨hal-01637944⟩
193 View
145 Download


Gmail Facebook X LinkedIn More