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Low-Degree Polynomial Approximation of the Cross-Polytope
We determine the degree-distortion tradeoff for polynomial approximation of the $d$-dimensional cross-polytope $B_1^d$. For every $1\le t\le d$, every globally nonnegative degree-$2t$ form that is positive away from the origin has multiplicative sandwich distortion at least $(2e)^{-1/2}\sqrt{d/t}$,
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