Gowers' Ramsey Theorem for generalized tetris operations

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:149

Article

Lupini, Martino¹ 

[1] CALTECH, Math Dept, 1200 E Calif Blvd,MC 253-37, Pasadena, CA 91125 USA

关键词: Gowers' Ramsey Theorem;    Hindman theorem;    Milliken-Taylor theorem;    Idempotent ultrafilter;    Stone-Cech compactification;    Partial semigroup;   

DOI  :  10.1016/j.jcta.2017.02.001

来源: Elsevier

【 摘 要 】

We prove a generalization of Cowers' theorem for FIN kappa where, instead of the single tetris operation T : FINk -> FINk-1, one considers all maps from FINk to FINj for 0 <= j <= k arising from nondecreasing surjections f : {0, 1,..., k} --+ {0,1,..., j}. This answers a question of Bartogova and Kwiatkowska. We also describe how to prove a common generalization of such a result and the Galvin-Glazer-Hindman theorem on finite products, in the setting of layered partial semigroups introduced by Farah, Hindman, and McLeod. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free