Polynomial bound for partition rank in terms of analytic rank

DOI10.1007/s00039-019-00505-4zbMath1442.11027arXiv1902.09830OpenAlexW2955654011WikidataQ127643473 ScholiaQ127643473MaRDI QIDQ2334613

Luka Milićević

Publication date: 7 November 2019

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.09830

zbMATH Keywords

partition rankanalytic rank

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (12)

The analytic rank of tensors and its applications ⋮ Approximately symmetric forms far from being exactly symmetric ⋮ Inverse theorem for certain directional Gowers uniformity norms ⋮ Partition and analytic rank are equivalent over large fields ⋮ On rank in algebraic closure ⋮ Relative rank and regularization ⋮ Subspaces of tensors with high analytic rank ⋮ Properties of high rank subvarieties of affine spaces ⋮ Applications of algebraic combinatorics to algebraic geometry ⋮ Unnamed Item ⋮ Polynomial bound for the partition rank vs the analytic rank of tensors ⋮ A note on extensions of multilinear maps defined on multilinear varieties

Cites Work

• Linear forms and higher-degree uniformity for functions on \(\mathbb F^n_p\)
• Linear equations in primes
• Improved bounds for the extremal number of subdivisions
• The partition rank of a tensor and \(k\)-right corners in \(\mathbb{F}_q^n\)
• Properties of high rank subvarieties of affine spaces
• Nonconventional ergodic averages and nilmanifolds
• The distribution of polynomials over finite fields, with applications to the Gowers norms
• The analytic rank of tensors and its applications
• A new proof of Szemerédi's theorem

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