# On generic and maximal $k$-ranks of binary forms

2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : In what follows, we pose two general conjectures about decompositions of homogeneous poly-nomials 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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Preprints, Working Papers, ...

Cited literature [27 references]

https://hal.inria.fr/hal-01637944
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Submitted on : Saturday, November 18, 2017 - 5:59:41 PM
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171113_LORS_arXiv.pdf
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• HAL Id : hal-01637944, version 1

### Citation

Samuel Lundqvist, Alessandro Oneto, Bruce Reznick, Boris Shapiro. On generic and maximal $k$-ranks of binary forms. 2017. ⟨hal-01637944⟩

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