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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13126 |
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| _version_ | 1866912489153757184 |
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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 |