The next gap in the subrank of 3-tensors

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-06 DOI:10.1016/j.laa.2025.04.027

Fulvio Gesmundo , Jeroen Zuiddam

引用次数: 0

Abstract

Recent works of Costa–Dalai, Christandl–Gesmundo–Zuiddam, Blatter–Draisma–Rupniewski, and Briët–Christandl–Leigh–Shpilka–Zuiddam have investigated notions of discreteness and gaps in the possible values that asymptotic tensor ranks can take. In particular, it was shown that the asymptotic subrank and asymptotic slice rank of any nonzero 3-tensor is equal to 1, equal to 1.88, or at least 2 (over any field), and that the set of possible values of these parameters is discrete (in several regimes). We determine exactly the next gap, showing that the asymptotic subrank and asymptotic slice rank of any nonzero 3-tensor is equal to 1, equal to 1.88, equal to 2, or at least 2.68.

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下一个3张量子分支的间隙

Costa-Dalai, Christandl-Gesmundo-Zuiddam， Blatter-Draisma-Rupniewski和Briët-Christandl-Leigh-Shpilka-Zuiddam最近的作品研究了渐近张量秩可能取值的离散性和间隙的概念。特别地，证明了任意非零3张量的渐近子分支和渐近片秩等于1，等于1.88，或至少等于2（在任意域上），并且这些参数的可能值的集合是离散的（在若干域中）。我们精确地确定了下一个间隙，证明了任意非零3张量的渐近子分支和渐近切片秩等于1，等于1.88，等于2，或至少等于2.68。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.