Maximal dimension of unit simplices

Christian Elsholtz; Walter Klotz

doi:10.1007/s00454-004-1155-x

Maximal dimension of unit simplices

Christian Elsholtz^*, Walter Klotz

^*Corresponding author for this work

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

Abstract

For an arbitrary field F the maximal number ω(Fⁿ) of points in Fⁿ mutually distance 1 apart with respect to the standard inner product is investigated. If the characteristic char(F) is different from 2, then the values of ω(Fⁿ) lie between n - 1 and n + 2. In particular, we answer completely for which n a simplex of q points with edge length 1 can be embedded in rational n-space. Our results imply for almost all even n that ω(Qⁿ) = n and for almost all odd n that ω(Qⁿ) = n - 1.

Original language	English
Pages (from-to)	167-177
Number of pages	11
Journal	Discrete & Computational Geometry
Volume	34
Issue number	1
DOIs	https://doi.org/10.1007/s00454-004-1155-x
Publication status	Published - 2005

ASJC Scopus subject areas

Theoretical Computer Science
Computational Theory and Mathematics
Discrete Mathematics and Combinatorics
Geometry and Topology

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10.1007/s00454-004-1155-x

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abstract = "For an arbitrary field F the maximal number ω(Fn) of points in Fn mutually distance 1 apart with respect to the standard inner product is investigated. If the characteristic char(F) is different from 2, then the values of ω(Fn) lie between n - 1 and n + 2. In particular, we answer completely for which n a simplex of q points with edge length 1 can be embedded in rational n-space. Our results imply for almost all even n that ω(Qn) = n and for almost all odd n that ω(Qn) = n - 1.",

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Maximal dimension of unit simplices

Abstract

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