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ON POINT SETS IN VECTOR SPACES OVER FINITE FIELDS THAT DETERMINE ONLY ACUTE ANGLE TRIANGLES

Part of: Discrete geometry Designs and configurations

Published online by Cambridge University Press:  21 October 2009

IGOR E. SHPARLINSKI
IGOR E. SHPARLINSKI*
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia (email: igor@ics.mq.edu.au)
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Abstract

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For three points , and in the n-dimensional space 𝔽nq over the finite field 𝔽q of q elements we give a natural interpretation of an acute angle triangle defined by these points. We obtain an upper bound on the size of a set 𝒵 such that all triples of distinct points define acute angle triangles. A similar question in the real space ℛn dates back to P. Erdős and has been studied by several authors.

Keywords

acute angle trianglefinite fieldcharacter sum

MSC classification

Secondary: 05B25: Finite geometries 52C10: Erdős problems and related topics of discrete geometry
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 114 - 120
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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