Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 52: Issue 3
A separation theorem for totally-sewn 4-polytopes
Authors:
T. Bisztriczky University of Calgary, 2500 University Dr. N.W., Calgary, Alberta, T2N 1N4, Canada

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and
F. Fodor University of Calgary, 2500 University Dr. N.W., Calgary, Alberta, T2N 1N4, Canada
University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

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Pages:
386–422
Online Publication Date:
Sep 2015
Publication Date:
01 Sep 2015
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2015.52.3.1316
Keywords:
Primary 52B11; Gohberg–Markus–Hadwiger covering number; neighbourly polytopes; separation problem; totally-sewn polytopes
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The Separation Problem, originally posed by K. Bezdek in [1], asks for the minimum number s(O, K) of hyperplanes needed to strictly separate an interior point O in a convex body K from all faces of K. It is conjectured that s(O, K) ≦ 2d in d-dimensional Euclidean space. We prove this conjecture for the class of all totally-sewn neighbourly 4-dimensional polytopes.

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    Bezdek, K. and Bisztriczky, T., Hadwiger’s covering conjecture and low-dimensional dual cyclic polytopes, Geom. Dedicata, 46 (1993), no. 3, 279–286.

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    Bezdek, K. and Bisztriczky, T., A proof of Hadwiger’s covering conjecture for dual cyclic polytopes, Geom. Dedicata, 68 (1997), no. 1, 29–41.

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    Bisztriczky, T. , Separation in neighbourly 4-polytopes, Studia Sci. Math. Hungar., 39 (2002), no. 3–4, 277–289.

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    Bisztriczky, T., Fodor, F. and Oliveros, D., Separation in totally-sewn 4-polytopes with the decreasing universal edge property, Beitäge Algebra Geom., 53 (2012), no. 1, 123–138.

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  • [6]

    Bisztriczky, T. and Oliveros, D., Separation in totally-sewn 4-polytopes, in: Discrete geometry, Monogr. Textbooks Pure Appl. Math., 253 Dekker (New York, 2003), 59–68.

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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)
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  • Márton NASZÓDI (ELTE, Budapest)
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  • Zoltán SZABÓ (Princeton University)
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  • 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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