Linear Dependence of Powers of Linear Forms

• Autorzy: Andrzej Sładek
• Języki publikacji: EN

Abstrakty

EN

The main goal of the paper is to examine the dimension of the vector space spanned by powers of linear forms. We also find a lower bound for the number of summands in the presentation of zero form as a sum of d-th powers of linear forms.(original abstract)

Słowa kluczowe

EN

Mathematics; Differential equations

PL

Matematyka; Równania różniczkowe

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Strony: 131--138

Twórcy

autor

Andrzej Sładek

• Institute of Mathematics University of Silesia

Bibliografia

• Białynicki-Birula A., Schinzel A., Representations of multivariate polynomials by sums of univariate polynomials in linear forms, Colloq. Math. 112 (2008), 201-233. [Corrigendum. Colloq. Math. 125 (2011), 139.]
• Chlebowicz A., Wołowiec-Musiał M., Forms with a unique representation as a sum of powers of linear forms, Tatra Mt. Math. Publ. 32 (2005), 33-39.
• Reznick B., Sums of even powers of real linear forms, Memoirs Amer. Math. Soc. 96 (1992), no. 463.
• Reznick B., Patterns of dependence among powers of polynomials, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 60 (2003), 101-121.

Identyfikatory

DOI

10.1515/amsil-2015-0010