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Markov Processes and Ramsey Theory for Trees

Published online by Cambridge University Press:  03 December 2003

Hillel Furstenberg  and
Benjamin Weiss
Hillel Furstenberg*
Affiliation:
Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
Benjamin Weiss*
Affiliation:
Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
*
(e-mail: harry@math.huji.ac.il)
(e-mail: weiss@math.huji.ac.il)
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Abstract

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We consider analogues of van der Waerden's theorem and Szemerédi's theorem, where arithmetic progressions are replaced by binary trees with a fixed distance between successive vertices. The proofs are based on some novel recurrence properties for Markov processes.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 12 , Issue 5-6: This issue contains volume twelve, parts five and six , November 2003 , pp. 547 - 563
Copyright
Copyright © Cambridge University Press 2003