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Bibliographic Details
Main Author: Kawabe, Daiki
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.13126
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author Kawabe, Daiki
author_facet Kawabe, Daiki
contents This note provides a detailed proof of Conner--Gesmundo--Landsberg--Ventura's result that the border rank of the Kronecker square of the little Coppersmith--Winograd tensor is $(q+2)^{2}$.We also indicate how the same ideas seem to extend to the case of the Kronecker cube, pointing toward the conjectural value $(q+2)^{m}$ for $m\ge 4$, although a full proof is left for future work.
format Preprint
id arxiv_https___arxiv_org_abs_2507_13126
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor
Kawabe, Daiki
Algebraic Geometry
This note provides a detailed proof of Conner--Gesmundo--Landsberg--Ventura's result that the border rank of the Kronecker square of the little Coppersmith--Winograd tensor is $(q+2)^{2}$.We also indicate how the same ideas seem to extend to the case of the Kronecker cube, pointing toward the conjectural value $(q+2)^{m}$ for $m\ge 4$, although a full proof is left for future work.
title Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor
topic Algebraic Geometry
url https://arxiv.org/abs/2507.13126