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On Helly Numbers for Crystals and Cut-And-Project Sets

Name: On Helly Numbers for Crystals and Cut-And-Project Sets
Creator: Garber, Alexey
Keywords: Mathematics - Metric Geometry, FOS: Mathematics, Mathematics - Combinatorics, Metric Geometry (math.MG), 0102 computer and information sciences, Combinatorics (math.CO), 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Nov 2024Embargo end date: 01 Jan 2016Publisher:Akademiai Kiado Zrt.Journal:Studia Scientiarum Mathematicarum Hungarica, volume 61, pages 203-214 (issn: 0081-6906, eissn: 1588-2896,

Authors: Garber, Alexey;

doi: 10.1556/012.2024.04314 , 10.48550/arxiv.1605.07881

arXiv: http://arxiv.org/abs/1605.07881

On Helly Numbers for Crystals and Cut-And-Project Sets

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Abstract

We prove existence of Helly numbers for crystals and for cut-and-project sets with convex windows. Also we show that for a two-dimensional crystal consisting of 𝑘 copies of a single lattice the Helly number does not exceed 𝑘 + 6.

Related Organizations

University of the West
United States
The University of Texas Rio Grande Valley
United States

Keywords

Mathematics - Metric Geometry, FOS: Mathematics, Mathematics - Combinatorics, Metric Geometry (math.MG), Combinatorics (math.CO)

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