Monomials as sums of powers: The real binary case

By M. Boij, Enrico Carlini, A. V. Geramita. 2010

46 citations recorded by the source corpus.

We generalize an example, due to Sylvester, and prove that any monomial of degree d in R[x(0), x(1)], which is not a power of a variable, cannot be written as a linear combination of fewer than d powers of linear forms.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0bf39e8fbfb469bbd7db9128da2dfc497fa6d26a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. M. Catalisano
2. Bruce Reznick
3. Alessandro Gimigliano
4. Alessandra Bernardi
5. Enrico Carlini

In Computational Theory and Mathematics

1. Bruce Reznick
2. Alessandra Bernardi
3. M. Catalisano
4. A. Oneto
5. Alessandro Gimigliano
6. Enrico Carlini
7. Monique Laurent
8. L. Fialkow

Citations in the corpus

• The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, methodology): “, d − 1, there exists ci’s such that f has d real distinct roots and cj = 0; see [225] (Lemma 4.”
• ON THE LENGTH OF BINARY FORMS (2010, background): “There has been a recent series of papers studying LR(f) [4, 9, 15]; these study the length in a greater depth than we do here.”