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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Partitioning $\alpha$–large sets: Some lower bounds
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by Teresa Bigorajska and Henryk Kotlarski PDF
Trans. Amer. Math. Soc. 358 (2006), 4981-5001 Request permission

Abstract:

Let $\alpha \rightarrow (\beta )_m^r$ denote the property: if $A$ is an $\alpha$–large set of natural numbers and $[A]^r$ is partitioned into $m$ parts, then there exists a $\beta$–large subset of $A$ which is homogeneous for this partition. Here the notion of largeness is in the sense of the so–called Hardy hierarchy. We give a lower bound for $\alpha$ in terms of $\beta ,m,r$ for some specific $\beta$.
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Additional Information
  • Teresa Bigorajska
  • Affiliation: Faculty of Mathematics, Cardinal Stefan Wyszyński University, ul. Dewajtis 5, 01–815 Warszawa, Poland
  • Email: tebigo@op.pl
  • Henryk Kotlarski
  • Affiliation: Faculty of Mathematics, Cardinal Stefan Wyszyński University, ul. Dewajtis 5, 01–815 Warszawa, Poland – and – Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, P.O. Box 137, 00–950 Warszawa, Poland
  • Email: hkl@impan.gov.pl
  • Received by editor(s): April 26, 2004
  • Received by editor(s) in revised form: October 18, 2004
  • Published electronically: June 15, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 4981-5001
  • MSC (2000): Primary 05A18
  • DOI: https://doi.org/10.1090/S0002-9947-06-03883-9
  • MathSciNet review: 2231881