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.

On generic and maximal k-ranks of binary forms / Lundqvist, S.; Oneto, A.; Reznick, B.; Shapiro, B.. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 223:5(2019), pp. 2062-2079. [10.1016/j.jpaa.2018.08.015]

On generic and maximal k-ranks of binary forms

Oneto A.;
2019

Abstract

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.
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Lundqvist, S.; Oneto, A.; Reznick, B.; Shapiro, B.
On generic and maximal k-ranks of binary forms / Lundqvist, S.; Oneto, A.; Reznick, B.; Shapiro, B.. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 223:5(2019), pp. 2062-2079. [10.1016/j.jpaa.2018.08.015]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/257255
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