ON THE LENGTH OF BINARY FORMS

By Bruce Reznick. 2010

59 citations recorded by the source corpus.

The K-length of a form f in \(K[x_{1},\ldots,x_{n}]\), \(K \subset \mathbb{C}\), is the smallest number of d-th powers of linear forms of which f is a K-linear combination. We present many results, old and new, about K-length, mainly for n = 2, and often about the length of the same form over different fields. For example, the K-length of \(3{x}^{5} - 20{x}^{3}{y}^{2} + 10x{y}^{4}\) is three for \(K = \mathbb{Q}(\sqrt{-1})\), four for \(K = \mathbb{Q}(\sqrt{-2})\) and five for \(K = \mathbb{R}\).

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/37efa63cef4921e9ef09b06cd183e099811aefca

Citations in the corpus

• The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, unknown): “binary forms any 1 d classical, [159] quadrics 2 any n+ 1 classical plane cubics 3 2 5 [160, 76] plane quartics 4 2 7 [162, 161] plane quintics 5 2 10 [163, 164] cubic surfaces 3 3 7 [160] cubic hypersurfaces 3 any ¬ ⌊ d(2)+6d+1 4 ⌋ [165]”