2024/08/14 by Paweł Pielasa, Pielasa, Paweł, Matouš Šafránek +3 · 1 citation
Engineering · #14N07 #15A69 #68Q17 #Algebraic Geometry (math.AG) #Computational Complexity (cs.CC) #Engineering and Materials Science Studies #FOS: Computer and information sciences #FOS: Mathematics #Physics and Engineering Research Articles
paper · pdf · doi:10.48550/arxiv.2408.07550
openalex publication_date 2024/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we prove the subrank of a generic tensor in ℂn,n,n to be Q(n) = \lfloor√(3n - 2)\rfloor by providing a lower bound to the known upper bound. More generally, we find the generic subrank of tensors of all orders and dimensions. This answers two open questions posed in arXiv:2205.15168v2. Finally, we compute dimensions of varieties of tensors of subrank at least r.