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Study of \(\kappa (D)\) for \(D = \{2, 3, x, y\}\)

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Combinatorial Algorithms (IWOCA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

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  • International Workshop on Combinatorial Algorithms

Abstract

Let D be a set of positive integers. The kappa value of D, denoted by \(\kappa (D)\), is the parameter involved in the so called “lonely runner conjecture.” Let x, y be positive integers, we investigate the kappa values for the family of sets \(D =\{2, 3, x, y\}\). For a fixed positive integer \(x > 3\), the exact values of \(\kappa (D)\) are determined for \(y=x+i\), \(1 \le i \le 6\). These results lead to some asymptotic behavior of \(\kappa (D)\) for \(D=\{2, 3, x, y\}\).

Supported in part by the National Science Foundation under grant DMS-1247679.

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Authors and Affiliations

  1. California State University Los Angeles, Los Angeles, CA, 90032, USA

    Daniel Collister & Daphne Der-Fen Liu

Authors
  1. Daniel Collister
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  2. Daphne Der-Fen Liu
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Corresponding author

Correspondence to Daphne Der-Fen Liu .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Collister, D., Liu, D.DF. (2015). Study of \(\kappa (D)\) for \(D = \{2, 3, x, y\}\) . In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_22

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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