2021/03/23 by Roser Homs, Homs, Roser, Joachim Jelisiejew +5
Computer Science · Mathematics · #14Q20 #15A69 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2103.12598
openalex publication_date 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassen's laser method and obtain an upper bound 2.431 on ω. We also explain how in certain monomial cases using the laser method directly is less profitable than first degenerating. Our results form possible paths in the search for valuable tensors for the laser method away from Coppersmith-Winograd tensors.