AN UPPER BOUND FOR THE HALES-JEWETT NUMBER HJ(4,2)

作者：Lavrov Mikhail^*

来源：SIAM Journal on Discrete Mathematics, 2016, 30(2): 1333-1342.

DOI：10.1137/15M1016485

• Ramsey theory
• Hales-Jewett theorem
• coloring
• grid

We show that for n at least 10(11), any 2-coloring of the n-dimensional grid [4](n) contains a monochromatic combinatorial line. This is a special case of the Hales-Jewett theorem [Hales and Jewett, Trans. Amer. Math., 106 (1963), pp. 222 229], to which the best known general upper bound is due to Shelah [J. Amer. Math. Soc., 1 (1988), pp. 683-697]; Shelah's recursion gives an upper bound between 2 up arrow up arrow 7 and 2 up arrow up arrow 8 for the case we consider, and no better value was previously known.

• 出版日期2016