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On the existence of U-polygons of class c≥4 in planar point sets

Huck, Christian (2009). On the existence of U-polygons of class c≥4 in planar point sets. Discrete Mathematics, 309(16) pp. 4977–4981.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.disc.2009.02.035
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Abstract

For a finite set U of directions in the Euclidean plane, a convex non-degenerate polygon P is called a U-polygon if every line parallel to a direction of U that meets a vertex of P also meets another vertex of P. We characterize the numbers of edges of U-polygons of class c≥4 with all their vertices in certain subsets of the plane and derive explicit results in the case of cyclotomic model sets.

Item Type: Journal Article
Copyright Holders: 2009 Elsevier B.V.
ISSN: 0012-365X
Project Funding Details:
Funded Project NameProject IDFunding Body
Combinatorics of Sequences and Tilings and its ApplicationsEP/D058465/1EPSRC (Engineering and Physical Sciences Research Council)
Keywords: algebraic Delone set; U-polygon; affinely regular polygon; cyclotomic model set
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 23224
Depositing User: Uwe Grimm
Date Deposited: 22 Sep 2010 15:22
Last Modified: 24 Mar 2014 13:55
URI: http://oro.open.ac.uk/id/eprint/23224
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