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Title: Linear dependence of powers of linear forms
Authors: Sładek, Andrzej
Keywords: Linear form; Sums of powers of linear forms; Ticket of the set of polynomials
Issue Date: 2015
Citation: Annales Mathematicae Silesianae, Nr 29 (2015), s. 131-138
Abstract: For a finite set of polynomials F={fj}, B. Reznick [in Algorithmic and quantitative real algebraic geometry (Piscataway, NJ, 2001), 101–121, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 60, Amer. Math. Soc., Providence, RI, 2003; MR1995017] introduced the ticket T(F)={d∈N:{fdj} is linearly dependent}. Motivated by results in the above paper, the author of the current paper studies the "degree'' of linear dependence of the set of powers of polynomials within its ticket, i.e., dimspan{fdj} for d∈T(F). This seems to be a rather difficult question for an arbitrary set of polynomials. The author therefore focuses on the special case when the polynomials are linear forms and proves various interesting results. The interested reader should consult the paper for the details.
DOI: 10.1515/amsil-2015-0010
ISSN: 0860-2107
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