Sums of squares of k-term forms

Charu Goel; Bruce Reznick

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arXiv · 2403.08697

Sums of squares of k-term forms

Charu Goel·Bruce Reznick

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Abstract

In this paper we study the cones corresponding to sums of squares of $n$-ary $d$-ic forms with at most $k$ terms. We show that these are strictly nested as $k$ increases, leading to the usual sum of squares cone. We also discuss the duals of these cones. For $n \ge 3$, we construct indefinite irreducible $n$-ary $d$-ic forms with exactly $k$ terms for $2 \le k \le \binom{n+d-1}{n-1}$.

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Charu Goel, Bruce Reznick. 2024-03-13. Sums of squares of k-term forms. https://arxiv.org/abs/2403.08697

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