42 citations · 129 across the 20 of their papers we have counts for
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On generic and maximal k-ranks of binary forms
Samuel Lundqvist, Alessandro Oneto, Bruce Reznick +1
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…
Binary forms with three different relative ranks
Bruce Reznick, Neriman Tokcan
Suppose is a binary form of degree with coefficients in a field . The -rank of is the smallest number of -th powers of linear forms ov…
The analogue of Hilbert's 1888 theorem for Even Symmetric Forms
Charu Goel, Salma Kuhlmann, Bruce Reznick
Hilbert proved in 1888 that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if or or , where is the number…
On the Choi-Lam analogue of Hilbert's 1888 theorem for Symmetric Forms
Charu Goel, Salma Kuhlmann, Bruce Reznick
A famous theorem of Hilbert from 1888 states that a positive semidefinite (psd) real form is a sum of squares (sos) of real forms if and only if or or , w…
Some new canonical forms for polynomials
Bruce Reznick
We give some new canonical representations for forms over $\cc$. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power o…
On Hilbert's construction of positive polynomials
Bruce Reznick
In 1888, Hilbert described how to find real polynomials in more than one variable which take only non-negative values but are not a sum of squares of polynomials. His construction…