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.;
2019-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
