Asymptotic Bounds on the Equilateral Dimension of Hypercubes

Lorenz Minder; Thomas Sauerwald; Sven Ake Wegner

doi:10.1007/s00373-014-1473-6

Asymptotic Bounds on the Equilateral Dimension of Hypercubes

Lorenz Minder, Thomas Sauerwald, Sven Ake Wegner

SCEDT Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1629-1636
Number of pages	8
Journal	Graphs and Combinatorics
Volume	31
Issue number	5
DOIs	https://doi.org/10.1007/s00373-014-1473-6
Publication status	Published - 24 Sept 2015

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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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AB - 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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Asymptotic Bounds on the Equilateral Dimension of Hypercubes

Abstract

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