Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 61: Issue 3
Remarks on Soft Ball Packings in Dimensions 2 and 3
Authors:
Károly Bezdek Department of Mathematics and Statistics, University of Calgary, Canada
Department of Mathematics, University of Pannonia, Veszprém, Hungary

Search for other papers by Károly Bezdek in
Current site
Google Scholar
PubMed Close
and
Zsolt Lángi MTA-BME Morphodynamics Research Group, Department of Algebra and Geometry, Budapest University of Technology and Economics, Budapest, Hungary

Search for other papers by Zsolt Lángi in
Current site
Google Scholar
PubMed Close
Pages:
251–261
Online Publication Date:
30 Sep 2024
Publication Date:
21 Nov 2024
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2024.04318
Keywords:
Euclidean 𝒅-space; Minkowski 𝒅-space; soft packing; soft parameter; soft density; soft lattice packing; FCC lattice; Voronoi decomposition; Delaunay decomposition; refined Molnár decomposition
Restricted access

We study translative arrangements of centrally symmetric convex domains in the plane (resp., of congruent balls in the Euclidean 3-space) that neither pack nor cover. We define their soft density depending on a soft parameter and prove that the largest soft density for soft translative packings of a centrally symmetric convex domain with 3-fold rotational symmetry and given soft parameter is obtained for a proper soft lattice packing. Furthermore, we show that among the soft lattice packings of congruent soft balls with given soft parameter the soft density is locally maximal for the corresponding face centered cubic (FCC) lattice.

  • [1]

    F. Aurenhammer, R. Klein and D.-T. Lee. Voronoi diagrams and Delaunay triangulations. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.

    • Search Google Scholar
    • Export Citation
  • [2]

    K. Bezdek and Z. Lángi. Density bounds for outer parallel domains of unit ball packings. Proc. Steklov Inst. Math., 288(1):209–225, 2015.

    • Search Google Scholar
    • Export Citation
  • [3]

    K. Böröczky. Closest packing and loosest covering of the space with balls, Studia Math. Sci. Hungar. 21 (1986), 79–89.

  • [4]

    K. Böröczky and L. Szabó. 12-neighbour packings of unit balls in 𝔼3. Acta Math. Hungar., 146(2):421–448, 2015.

  • [5]

    B. Csikós. On the volume of the union of balls. Discrete Comput. Geom., 20:449–461, 1998.

  • [6]

    H. Edelsbrunner and M. Iglesias-Ham. On the optimality of the FCC lattice for soft sphere packing. SIAM J. Discrete Math., 32(1):750–782, 2018.

    • Search Google Scholar
    • Export Citation
  • [7]

    L. Fejes Tóth. Some packing and covering theorems. Acta Sci. Math. (Szeged), 12:62–67, 1950.

  • [8]

    T. C. Hales and S. McLaughlin. The Dodecahedral Conjecture. J. Amer. Math. Soc., 23:299–344, 2010.

  • [9]

    T. Lambert. Empty shape triangulation algorithms. PhD thesis, University of Manitoba, 1994.

  • [10]

    J. Molnár. On the 𝜌-system of unit circles. Ann. Univ. Sci. Budapest, Eötvös Sect. Math., 20:195–203, 1977.

  • [11]

    C. A. Rogers. The closest packing of convex two-dimensional domains. Acta Math., 86:309–321, 1951.

  • [12]

    C. A. Rogers. Erratum to: The closest packing of convex two-dimensional domains, corrigendum. Acta Math., 104:305–306, 1960.

  • [13]

    Ch. Zong. The simultaneous packing and covering constants in the plane. Adv. Math., 218(3):653–672, 2008.

  • Collapse
  • Expand
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) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • 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")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu

Indexing and Abstracting Services:

  • CABELLS Journalytics
  • CompuMath Citation Index
  • Essential Science Indicators
  • Mathematical Reviews
  • Science Citation Index Expanded (SciSearch)
  • SCOPUS
  • Zentralblatt MATH

2024  
Scopus  
CiteScore  
CiteScore rank  
SNIP  
Scimago  
SJR index 0.305
SJR Q rank Q3

2023  
Web of Science  
Journal Impact Factor 0.4
Rank by Impact Factor Q4 (Mathematics)
Journal Citation Indicator 0.49
Scopus  
CiteScore 1.3
CiteScore rank Q2 (General Mathematics)
SNIP 0.705
Scimago  
SJR index 0.239
SJR Q rank Q3

Studia Scientiarum Mathematicarum Hungarica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article (only for OA publications)
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2025 Online subsscription: 796 EUR / 876 USD
Print + online subscription: 900 EUR / 988 USD
Subscription Information Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

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)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Nov 2024 122 9 10
Dec 2024 24 6 8
Jan 2025 100 1 3
Feb 2025 95 2 4
Mar 2025 82 1 1
Apr 2025 37 0 0
May 2025 21 0 0