Linear Dependence Of Powers Of Linear Forms
Annales Mathematicae Silesianae (2015)
- Volume: 29, Issue: 1, page 131-138
- ISSN: 0860-2107
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Abstract
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topAndrzej Sładek. "Linear Dependence Of Powers Of Linear Forms." Annales Mathematicae Silesianae 29.1 (2015): 131-138. <http://eudml.org/doc/276939>.
@article{AndrzejSładek2015,
abstract = {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.},
author = {Andrzej Sładek},
journal = {Annales Mathematicae Silesianae},
keywords = {linear form; sums of powers of linear forms; ticket of the set of polynomials},
language = {eng},
number = {1},
pages = {131-138},
title = {Linear Dependence Of Powers Of Linear Forms},
url = {http://eudml.org/doc/276939},
volume = {29},
year = {2015},
}
TY - JOUR
AU - Andrzej Sładek
TI - Linear Dependence Of Powers Of Linear Forms
JO - Annales Mathematicae Silesianae
PY - 2015
VL - 29
IS - 1
SP - 131
EP - 138
AB - 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.
LA - eng
KW - linear form; sums of powers of linear forms; ticket of the set of polynomials
UR - http://eudml.org/doc/276939
ER -
References
top- [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] Zbl1154.11011
- [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. Zbl1150.11417
- [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. Zbl1037.11022
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