This note proves border rank for Kronecker square; extends ideas to Kronecker cube, suggesting conjectural values.
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≥ 4, although a full proof is left for future work.
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Daiki Kawabe (2025) studied this question.
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