Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 61: Issue 3
On Helly Numbers for Crystals and Cut-And-Project Sets
Author:
Alexey Garber School of Mathematical & Statistical Sciences, The University of Texas Rio Grande Valley, 1 West University blvd., Brownsville, TX 78520, USA

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Pages:
203–214
Online Publication Date:
01 Oct 2024
Publication Date:
21 Nov 2024
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2024.04314
Keywords:
Helly-type theorem; lattice; periodic sets; cut-and-project
Restricted access

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.

  • [1]

    N. Amenta, J. A. De Loera, and P. Soberón. Helly’s Theorem: New Variations and Applications. In H. A. Harrington, M. Omar, and M. Wright, editors, Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics, 685, 55–95. American Mathematical Society, 2017.

    • Search Google Scholar
    • Export Citation
  • [2]

    G. Averkov. On Maximal 𝑆-Free Sets and the Helly Number for the Family of S-Convex Sets. SIAM J. Discrete Math., 27(3):1610–1624, 2013.

    • Search Google Scholar
    • Export Citation
  • [3]

    G. Averkov and R. Weismnatel. Transversal numbers over subsets of linear spaces. Adv. Geom., 12:19–28, 2012.

  • [4]

    M. Baake. A Guide to Mathematical Quasicrystals. In J.-B. Suck, M. Schreiber, and P. Häussler, editors, Quasicrystals – An Introduction of Structure, Physical Properties and Applications, 17–48. Springer, Berlin, 2002.

    • Search Google Scholar
    • Export Citation
  • [5]

    M. Baake and U. Grimm. Aperiodic Order. Vol. 1: A Mathematical Invitation. Cambridge University Press, Cambridge, 2013.

  • [6]

    I. Bárány and J. Matoušek. A fractional Helly theorem for convex lattice sets. Adv. Math., 174:227–235, 2003.

  • [7]

    F. P. M. Beenker. Algebraic theory of non-periodic tilings of the plane by two simple building blocks: a square and a rhombus. Eindhoven University of Technology, 1982, TH-Report, 82-WSK04.

    • Search Google Scholar
    • Export Citation
  • [8]

    N. G. de Bruijn. Algebraic theory of Penrose’s nonperiodic tilings of the plane. I, II. Nederl. Akad. Wetensch. Indag. Math., 43(1):39–66, 39–52, 53–66, 1981.

    • Search Google Scholar
    • Export Citation
  • [9]

    J. A. De Loera, R. N. La Haye, D. Oliveros, and E. Roldán-Pensado. Helly numbers of algebraic subsets of ℝ𝑑 and an extension of Doignon’s Theorem. Adv. Geom., 17(4):473–482, 2017.

    • Search Google Scholar
    • Export Citation
  • [10]

    J.-P. Doignon. Convexity in crystallographical lattices. J. Geom., 3:71–85, 1973.

  • [11]

    D. Frettlöh, F. Gähler, and E. Harris. Tilings Encyclopedia. http://tilings.math.uni-bielefeld.de/.

  • [12]

    A. Glazyrin. Private communication. May 2016.

  • [13]

    E. Helly. Über Mengen konvexer Körper mit gemeinschaftlichen Punkten. Jahresbericht der Deutschen Mathematiker-Vereinigung, 32:175–176, 1923.

    • Search Google Scholar
    • Export Citation
  • [14]

    R. V. Moody. Model sets: A survey. In F. Axel, F. Dénoyer, J. P. Gazeau, editors, From Quasicrystals to More Complex Systems. EDP Sciences, Les Ulis, and Springer, Berlin, 2000, 145–166.

    • Search Google Scholar
    • Export Citation
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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

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Gábor SÁGI (Rényi Institute of Mathematics)

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  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
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  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
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  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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