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Integers


Mathematical Citation Quotient (MCQ) 2016: 0.40

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1867-0660
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On a Variant of Van Der Waerden's Theorem

Sujith Vijay
  • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. E-mail:
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Published Online: 2010-05-31 | DOI: https://doi.org/10.1515/integ.2010.017

Abstract

Given positive integers n and k, a k-term quasi-progression of diameter n is a sequence (x 1, x 2, …, xk ) such that dx j+1xj d + n, 1 ≤ jk – 1, for some positive integer d. Thus an arithmetic progression is a quasi-progression of diameter 0. Let Qn (k) denote the least integer for which every coloring of {1, 2, …, Qn (k)} yields a monochromatic k-term quasi-progression of diameter n. We obtain an exponential lower bound on Q 1(k) using probabilistic techniques and linear algebra.

Keywords.: Ramsey theory; generalized arithmetic progressions; probabilistic method

About the article

Received: 2009-11-06

Published Online: 2010-05-31

Published in Print: 2010-05-01


Citation Information: Integers, Volume 10, Issue 2, Pages 223–227, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2010.017.

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