English

Shelah's partition functions and the Hales-Jewett numbers

Combinatorics 2021-07-06 v2

Abstract

In this paper we study several partition relations, defined by Saharon Shelah, and relate them to the Hales-Jewett numbers. In particular we give an upper bound for the Hales-Jewett numbers using the primitive recursive function f8,\mathtt{f}^{8,*} which belongs to the class E5\mathcal{E}^5 of the Grzegorczyk hierarchy and grows slower than the function f13\mathtt{f}^{13}. This improves the recent result of the first author and Shelah.

Keywords

Cite

@article{arxiv.2104.05962,
  title  = {Shelah's partition functions and the Hales-Jewett numbers},
  author = {Mohammad Golshani and Mostafa Mirabi},
  journal= {arXiv preprint arXiv:2104.05962},
  year   = {2021}
}