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Analysis reveals upper bounds on border ranks of twisted powers, suggesting applications in complexity theory.
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that they are optimal under mild conditions. We give applications to complexity theory. Many of the results rest on the notion of an encompassing polynomial, which we introduce.
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Flavi et al. (2025) studied this question.
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