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The slice rank of a direct sum

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arxiv 2105.08394 v2 pith:BZVFLJD6 submitted 2021-05-18 math.CO

classification math.CO
keywords slicerankbounddirectequaltensordiagonalentries
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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

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Two-Cut Coherence of Quintic Forms: Lifting Separations and Second-Derivative Completeness

    cs.CC 2026-08 accept novelty 7.0 of 10

    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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