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.

Słowa kluczowe

EN

linear form; sums of powers of linear forms; ticket of the set of polynomials

Kategorie tematyczne

• 11E76: Forms of degree higher than two
• 15A99: Miscellaneous topics

• Wydawca: De Gruyter Open
• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Numer: 1
• Strony: 131-138

Daty

wydano

2015-09-01

otrzymano

2015-01-06

poprawiono

2015-05-12

online

2015-09-30

Twórcy

autor

Andrzej Sładek

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] 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.][Crossref]
• [2] 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.
• [3] Reznick B., Sums of even powers of real linear forms, Memoirs Amer. Math. Soc. 96 (1992), no. 463.
• [4] 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