This paper presents a construction for symmetric, non-negative polynomials, which are not sums of squares. It explicitly generalizes the Motzkin polynomial and the Robinson polynomials to families of non-negative polynomials, which are not sums of squares. The degrees of the resulting polynomials can be chosen in advance.

polynomial, sums of squares, SOS, PSD, polynomial optimization"
Computational aspects of field theory and polynomials (msc 12Y05), Representations of finite symmetric groups (msc 20C30), Polynomials: location of zeros (algebraic theorems) (msc 12D10), Polynomials: location of zeros (msc 26C10), Special polynomials (msc 12E10)
Logistics (theme 3)
CWI
CWI. Probability, Networks and Algorithms [PNA]
Networks and Optimization

Bosse, H. (2007). Symmetric, positive polynomials, which are not sums of squares. CWI. Probability, Networks and Algorithms [PNA]. CWI.