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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The cardinality of some symmetric differences
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by Po-Yi Huang, Wen-Fong Ke and Günter F. Pilz PDF
Proc. Amer. Math. Soc. 138 (2010), 787-797 Request permission

Abstract:

In this paper, we prove that for positive integers $k$ and $n$, the cardinality of the symmetric differences of $\{1,2,\dots ,k\}$, $\{2,4,\dots ,2k\}$, $\{3,6,\dots ,3k\}$, …, $\{n,2n,\dots ,kn\}$ is at least $k$ or $n,$ whichever is larger. This solved a problem raised by Pilz in which binary composition codes were studied.
References
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Additional Information
  • Po-Yi Huang
  • Affiliation: Department of Mathematics and National Center for Theoretical Sciences (South), National Cheng Kung University, 1 University Road, Tainan 701, Taiwan
  • Email: pyhuang@mail.ncku.edu.tw
  • Wen-Fong Ke
  • Affiliation: Department of Mathematics and National Center for Theoretical Sciences (South), National Cheng Kung University, 1 University Road, Tainan 701, Taiwan
  • Email: wfke@mail.ncku.edu.tw
  • Günter F. Pilz
  • Affiliation: Department of Algebra, Johannes Kepler Universität Linz, Altenberger Strasse 69, 4040 Linz, Austria
  • Email: guenter.pilz@jku.at
  • Received by editor(s): June 1, 2009
  • Published electronically: October 23, 2009
  • Additional Notes: The first author was supported by the National Science Council, Taiwan, grant #96-2115-M-006-003-MY3
    The second author was partially supported by the National Science Council, Taiwan, grant #97-2923-M-006-001-MY2
    The third author was supported by grant P19463 of the Austrian National Science Fund (FWF)
  • Communicated by: Jim Haglund
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 787-797
  • MSC (2010): Primary 05A05; Secondary 11N05, 94B05
  • DOI: https://doi.org/10.1090/S0002-9939-09-10189-2
  • MathSciNet review: 2566544