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The slice rank of a direct sum
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We show that the slice rank of the direct sum of two tensors is equal to the sum of their slice ranks. The upper bound is trivial, but the lower bound needs more than a one-line proof, for reasons we explain. This result generalizes the fact, shown by Tao, that the slice rank of a diagonal tensor is equal to the number of non-zero entries of that tensor.
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Cited by 1 Pith paper
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Two-Cut Coherence of Quintic Forms: Lifting Separations and Second-Derivative Completeness
Two-cut coherence of a polynomial equals the minimal shared interface width for two degree cuts, and for quintics it is characterized up to constants by the slice rank of second derivatives.
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