AI 中文总结
该研究改进了拉姆齐数的代数构造，给出显式下界，提升了非对角及对角情形的界，得到R(33,t)≥t^{2.1-o(1)}，是首个证明固定s时R(s,t)≥t^c（c>2）的显式构造。
AI 中文摘要
我们给出了一种显式代数构造，表明对于满足3≤s≤t的整数，当t→∞时，R(s,t)≥t^{(1-o(1))log s / log(log s + 1)}。对于大的固定s，该构造改进了Alon与Pudlák的一般非对角构造中对s的依赖关系。特别地，R(33,t)≥t^{2.1-o(1)}，据我们所知，这是首个对某个固定s和某个c>2，证明R(s,t)≥t^c的显式构造。在对角情形下，它将经典Frankl-Wilson界指数中的主导常数从1/4提升至1，同时描述起来几乎同样简单。
英文摘要
We provide an explicit algebraic construction showing that, uniformly for integers $3 \leq s \leq t$, as $t \to \infty$, \[ R( s,t ) \geq t^{(1-o(1)) \log s / \log(\log s + 1) }. \] For large fixed $s$, this improves the dependence on $s$ in the general off-diagonal construction of Alon and Pudlák. In particular, $R(33, t) \geq t^{2.1-o(1)}$, to our knowledge, the first explicit construction showing $R(s, t) \geq t^c$ for some fixed $s$ and some $c > 2$. In the diagonal case, it improves the leading constant in the exponent of the classical Frankl--Wilson bound from $1/4$ to $1$, while being almost as simple to describe.
Comments10 pages
