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Gowers' Ramsey Theorem for generalized tetris operations

Lupini, Martino (2017) Gowers' Ramsey Theorem for generalized tetris operations. Journal of Combinatorial Theory. Series A, 149 . pp. 101-114. ISSN 0097-3165. doi:10.1016/j.jcta.2017.02.001.

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We prove a generalization of Gowers' theorem for FIN_k where, instead of the single tetris operation T:FIN_k→FIN_(k−1), one considers all maps from FIN_k to FIN_j for 0≤j≤k arising from nondecreasing surjections f:{0,1,…,k}→{0,1,…,j}. This answers a question of Bartošová 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.

Item Type:Article
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Lupini, Martino0000-0003-1588-7057
Additional Information:© 2017 Elsevier Inc. Received 6 April 2016, Available online 20 February 2017. We are grateful to David Fernandez, Aleksandra Kwiatkowska, Sławomir Solecki, and Kostas Tyros for their comment and suggestions. We are also thank Aleksandra Kwiatkowska for pointing out a mistake in an earlier version of this paper, and Ilijas Farah for referring us to [3] and to the theory of layered partial semigroups.
Subject Keywords:Gowers' Ramsey Theorem; Hindman theorem; Milliken–Taylor theorem; Idempotent ultrafilter; Stone–Čech compactification; Partial semigroup
Classification Code:2000 Mathematics Subject Classification. Primary 05D10; Secondary 54D80
Record Number:CaltechAUTHORS:20170427-113519614
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Official Citation:Martino Lupini, Gowers' Ramsey Theorem for generalized tetris operations, Journal of Combinatorial Theory, Series A, Volume 149, July 2017, Pages 101-114, ISSN 0097-3165, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77008
Deposited By: Tony Diaz
Deposited On:27 Apr 2017 19:07
Last Modified:15 Nov 2021 17:04

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