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On the Schmidt and analytic ranks for trilinear forms

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arxiv 2102.03659 v1 pith:AXXG37EJ submitted 2021-02-06 math.AG math.CO

Karim Adiprasito , David Kazhdan , Tamar Ziegler This is my paper · ORCID
classification math.AGmath.CO
keywords formsranksanalyticschmidttrilineardifferentdiscussessentially
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We discuss relations between different notions of ranks for multilinear forms. In particular we show that the Schmidt and the analytic ranks for trilinear forms are essentially proportional.

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Cited by 2 Pith papers

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

  1. Slice rank and partition rank of the determinant

    math.CO 2025-09 conditional novelty 8.0 of 10

    The determinant has slice rank n, partition rank at least log2(n)+1, and the 4x4 determinant has partition rank 3, giving the first unbounded separation between partition rank and analytic rank.

  2. Strength and partition rank under limits and field extensions

    math.AG 2025-02 conditional novelty 6.0 of 10

    For fixed degree d, strength and partition rank over any field are bounded by O(r^{d-1}) (plus a log factor on finite fields) in terms of their border rank analogues.

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