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: https://doi.org/10.1016/j.disc.2009.02.035

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.

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