An upper bound for the Waring rank of a form

2013/05/29 by Jelisiejew, Joachim
#13P05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.6957

Abstract

In this paper we introduce the open Waring rank of a form of degree d in n variables and prove the that this rank in bounded from above by \binomn+d-2d-1 - \binomn+d-6d-3 whenever n, d >= 3. This proves the same upper bound for the classical Waring rank of a form, improving the result of [BBS] and giving, as far as we know, the best upper bound known.

Related

• Some examples of forms of high rank
• On the Waring rank of binary forms: The binomial formula and a dihedral cover of rank two forms
• On the Waring Rank of Binary Forms
• Waring rank of binary forms, harmonic cross-ratio and golden ratio
• The Waring Rank of Ternary Cubic Forms