On generic and maximal k-ranks of binary forms

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dc.contributor.author	Lundqvist, Samuel
dc.contributor.author	Oneto, Alessandro
dc.contributor.author	Reznick, Bruce
dc.contributor.author	Shapiro, Boris
dc.date	2019-05-01
dc.identifier.citation	Lundqvist, S. [et al.]. On generic and maximal k-ranks of binary forms. "Journal of pure and applied algebra", 1 Maig 2019, vol. 223, núm. 5, p. 2062-2079.
dc.identifier.citation	0022-4049
dc.identifier.citation	https://arxiv.org/pdf/1711.05014.pdf
dc.identifier.citation	10.1016/j.jpaa.2018.08.015
dc.identifier.uri	http://hdl.handle.net/2117/129346
dc.language.iso	eng
dc.relation	https://www.sciencedirect.com/science/article/pii/S0022404918302123
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject	Polynomials
dc.subject	Polinomis
dc.title	On generic and maximal k-ranks of binary forms
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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.
dc.description.abstract	Peer Reviewed