AI 中文总结
研究哈雷-朱厄特数及其变体，通过计算、枚举和概率论证，给出组合几何变体的改进下界公式，还得出在5维超立方体上玩《四子连珠》可平局的结论。
AI 中文摘要
我们通过计算、枚举和概率论证来研究哈雷-朱厄特数及其一些变体。特别地，给出了哈雷-朱厄特数的组合几何变体的改进下界公式。作为所研究变体之一的结果，我们表明在任意边长的5维超立方体上由2人玩的米尔顿·布拉德利游戏《四子连珠》可以以平局结束。
英文摘要
We investigate the Hales-Jewett numbers and some variants of them, both computationally and via enumerative and probabilistic arguments. In particular, we give the improved lower bound formula on the combinatorial-geometric variant of the Hales-Jewett numbers. {As a consequence of one of the variants investigated, we show that the Milton Bradley game Connect Four played with 2 players on a 5-dimensional hypercube of any side length can end in a draw.
