Asymptotic Bounds on the Equilateral Dimension of Hypercubes

Asymptotic Bounds on the Equilateral Dimension of Hypercubes

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 a...

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Veröffentlicht in:Graphs and combinatorics 2015-09, Vol.31 (5), p.1629-1636
Hauptverfasser: Minder, Lorenz, Sauerwald, Thomas, Wegner, Sven-Ake
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic methods
Combinatorics
Engineering Design
Graph representations
Graphs
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung: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.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-014-1473-6