发表机构
The Hebrew University of Jerusalem; Rutgers University（耶路撒冷希伯来大学; 罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究哈雷 - 朱厄特数，核心方法是改进基于字母表大小归纳步骤为2 - 指数运算，主要贡献是将哈雷 - 朱厄特数边界改进为指数塔形式，还涉及相关定理及密度版本等。
AI 中文摘要
我们将哈雷 - 朱厄特数的边界改进为指数塔形式。此前是$WaW$（即本身为迭代指数运算的塔的迭代）。我们将归纳步骤（基于字母表大小$|\Lambda|$进行归纳）改进为2 - 指数运算，而非塔形式。在较长的打字工作中，(A)我们将此归纳步骤本身作为一个划分定理呈现；(B)我们将处理具有类似边界的哈雷 - 朱厄特密度版本。我们还在处理格雷厄姆 - 罗斯柴尔德定理、仿射拉姆齐定理及多项式情形，并给出背景。
英文摘要
We improve the bounds on the Hales-Jewett numbers to a tower of exponentiations. Earlier it was $WaW$ (that is, iterations of towers which are themselves iterated exponentiations). We improve the inductive step there (induction on the size of the alphabet, $|Λ|$) to 2-exponentiations, instead of towers. In the longer work in typing, (A) We present this inductive step as a partition theorem in its own right; (but in this preliminary version we make it just serve the bound on HJ numbers). (B) We shall deal with the density version of Hales-Jewett with similar bound. We are also dealing with the Graham-Rothschild Theorem and the Affine Ramsey Theorem and the polynomial case, and give background.
