Sets of points determining only acute angles and some related colouring problems

David Bevan

Sets of points determining only acute angles and some related colouring problems

David Bevan

Computer And Information Sciences

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7 Citations (Scopus)

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Abstract

We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ R^d such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}^d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.

Original language	English
Article number	R12
Number of pages	24
Journal	The Electronic Journal of Combinatorics
Volume	13
Issue number	1
Publication status	Published - 15 Feb 2006

Keywords

point sets
probabilistic method
acute angles

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title = "Sets of points determining only acute angles and some related colouring problems",

abstract = "We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ \{0, 1\}d. These results improve upon a probabilistic lower bound of Erd{\H o}s and F{\"u}redi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.",

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N2 - We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.

AB - We present both probabilistic and constructive lower bounds on the maximum size of a set of points S ⊆ Rd such that every angle determined by three points in S is acute, considering especially the case S ⊆ {0, 1}d. These results improve upon a probabilistic lower bound of Erdős and Füredi. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.

KW - point sets

KW - probabilistic method

KW - acute angles

UR - http://www.combinatorics.org/

UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/v13i1r12

M3 - Article

SN - 1077-8926

VL - 13

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

IS - 1

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ER -

Sets of points determining only acute angles and some related colouring problems

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Keywords

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