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arXiv · 2507.13126

Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor

Daiki Kawabe
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Abstract

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.

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Daiki Kawabe. 2025-07-17. Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor. https://arxiv.org/abs/2507.13126

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