On generic and maximal k-ranks of binary forms

In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number of variables. The second one (by the fourth a...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2019-05, Vol.223 (5), p.2062-2079
Main Authors: Lundqvist, Samuel, Oneto, Alessandro, Reznick, Bruce, Shapiro, Boris
Format: Article
Language:English
Subjects:
Matemàtiques i estadística
Polinomis
Polynomials
Àlgebra
Àrees temàtiques de la UPC
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Summary:In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number of variables. The second one (by the fourth author) deals with the maximal k-rank of binary forms. We settle the first conjecture in the cases of two variables and the second in the first non-trivial case of the 3-rd powers of quadratic binary forms.
ISSN:0022-4049
1873-1376
1873-1376
DOI:10.1016/j.jpaa.2018.08.015