$(2,n,m)$ 矩阵乘法的张量秩的新下界与GPT-6
New lower bounds on tensor rank of $(n,2,m)$ matrix multiplication with GPT-6
AI总结：
本文给出了$(2,n,m)$矩阵乘法张量秩的新下界：$n\ge4$时为$(n+2)m$，$n=3$时为$\lceil24m/5\rceil$，适用于任意域。
AI中文摘要：
对于$2\times n$与$n\times m$矩阵乘法，当$n\ge 4$时其张量秩至少为$(n+2)m$；当$n=3$时至少为$\left\lceil \frac{24}{5}m \right\rceil$。这两个下界在任意域上均成立。
英文摘要：
The tensor rank of $n\times 2$-with-$2\times m$ matrix multiplication is at least $(n+2)m$ if $n\ge 4$ and at least $\left\lceil \frac{24m+2}{5} \right\rceil$ if $n=3$, over arbitrary fields. This result matches the Hopcroft-Kerr upper bound for $n=3$ and $m\le 6$.
