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Asymptotic Bounds on the Equilateral Dimension of Hypercubes

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Abstract

A subset of the finite dimensional hypercube is said to be equilateral if the distance of any two distinct points equals a fixed value. The equilateral dimension of the hypercube is defined as the maximal size of its equilateral subsets. We study asymptotic bounds on the latter quantity considered as a function of two variables, namely dimension and distance.

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Authors and Affiliations

  1. Computer Science Division, University of California, Berkeley, CA, 94720-1776, USA

    Lorenz Minder

  2. Computer Lab., University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0FD, UK

    Thomas Sauerwald

  3. Bergische Universität Wuppertal, FB C—Mathematik, Gaußstr. 20, 42119, Wuppertal, Germany

    Sven-Ake Wegner

Authors
  1. Lorenz Minder
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  2. Thomas Sauerwald
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  3. Sven-Ake Wegner
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Correspondence to Sven-Ake Wegner.

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Minder, L., Sauerwald, T. & Wegner, SA. Asymptotic Bounds on the Equilateral Dimension of Hypercubes. Graphs and Combinatorics 31, 1629–1636 (2015). https://doi.org/10.1007/s00373-014-1473-6

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  • DOI: https://doi.org/10.1007/s00373-014-1473-6

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