Table of Contents
Geometry
Volume 2013, Article ID 715907, 2 pages
http://dx.doi.org/10.1155/2013/715907
Research Article

An Upper Bound for the Symmetric Tensor Rank of a Low Degree Polynomial in a Large Number of Variables

Department of Mathematics, University of Trento, 38123 Povo, Italy

Received 22 December 2012; Accepted 15 February 2013

Academic Editor: Michel Planat

Copyright © 2013 E. Ballico. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fix integers and . Let be a degree homogeneous polynomial in variables. Here, we prove that is the sum of at most -powers of linear forms (of course, this inequality is nontrivial only if .)