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Uniform stability of ranks

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arxiv 2411.03412 v1 pith:YZOJUDAI submitted 2024-11-05 math.CO

Guy Moshkovitz , Daniel G. Zhu This is my paper · ORCID
classification math.CO
keywords fieldanalysisanalyticassumingassumptionbasecarefulchen
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Chen and Ye recently proved that the analytic rank of tensors is stable under field extensions, assuming a fixed base field. Using a more careful analysis, we show that this assumption is unnecessary.

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  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.

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