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Periodica Mathematica Hungarica
Volume/Issue:
Volume 53: Issue 1-2
DOI:
https://doi.org/10.1007/s10998-006-0029-9
Author:
A. Heppes

Summary  

The problem of covering a circle, a square or a regular triangle with \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document} congruent circles of minimum diameter (the {\it circle covering} problem) has been investigated by a number of authors and the smallest diameter has been found for several values of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n$ \end{document} . This paper is devoted to the study of an analogous problem, the {\it diameter covering} problem, in which the shape and congruence of the covering pieces is relaxed and -- invariably -- the maximal diameter of the pieces is minimized. All cases are considered when the solution of the first problem is known and in all but one case the diameter covering problem is solved.

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 25: Issue 3
DOI:
https://doi.org/10.1007/bf02332831
Author:
P. Spyrou

Abstract  

A concept of finite coverings of continua with a linear order of their members is given. A characterization is obtained of hereditarily locally connected continua which have a finite supremum of cardinalities of the considered coverings.

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 60: Issue 4
DOI:
https://doi.org/10.1556/012.2023.04300
Authors:
András Bezdek
and
Włodzimierz Kuperberg

REFERENCES [1] A . Bezdek and W . Kuperberg . Unavoidable Crossings in a Thinnest Plane Covering with Congruent Convex Disks . Discrete Comput. Geom ., 43 : 187 – 208 , 2010 . [2] L . Fejes Tóth . Some packing and covering theorems . Acta

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 45: Issue 1-2
DOI:
https://doi.org/10.1023/a:1022310416382
Authors:
Uwe Schnell
and
Achill Schürmann
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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Accepted Manuscript / Online First
DOI:
https://doi.org/10.1556/012.2024.04316
Author:
András Bezdek

REFERENCES [1] J. H . Conway and S . Torquato . Packing, tiling, and covering with tetrahedra . Proc. Natl. Acad. Sci. USA , 103 : 10612 - 10617 , 2006 . [2] R . Dougherty and V . Faber . The degree-diameter problem for several

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Acta Mathematica Hungarica
Volume/Issue:
Volume 133: Issue 4
DOI:
https://doi.org/10.1007/s10474-011-0088-0
Authors:
Wenbin Guo
and
Alexander N. Skiba

– 18 10.1007/BF01313488 . [5] Guo , W. , Shum , K. P. , Skiba , A. N. 2003 G -covering subgroup systems for the classes of supersoluble and nilpotent groups Israel J. Math. 138 125

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Acta Mathematica Hungarica
Volume/Issue:
Volume 125: Issue 3
DOI:
https://doi.org/10.1007/s10474-009-9015-z
Author:
J. Januszewski

Abstract  

An equilateral triangle T e of sides 1 can be parallel covered with any sequence of squares whose total area is not smaller than 1:5. Moreover, any sequence of squares whose total area does not exceed
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{3} {4}(2 - \sqrt 3 )$$ \end{document}
(2 − √3) can be parallel packed into T e .
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Acta Mathematica Hungarica
Volume/Issue:
Volume 119: Issue 1-2
DOI:
https://doi.org/10.1007/s10474-007-7011-8
Authors:
Y. Konami
and
T. Miwa

Abstract  

By using coverings we introduce the concepts of fibrewise covering uniform space and its generalizations (fibrewise generalized uniform space and fibrewise semi-uniform space), and study the fibrewise completions of fibrewise generalized uniform spaces and fibrewise semi-uniform spaces.

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 61: Issue 2
DOI:
https://doi.org/10.1556/012.2024.04313
Authors:
Zhanjun Su
and
Yufang Wu

REFERENCES [1] J . Januszewski . Translative covering by sequences of homothetic copies . Acta Math. Hungar ., 91 ( 4 ): 337 – 342 , 2001 . [2] J . Januszewski . Parallel packing and covering of an equilateral triangle with sequences of

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 40: Issue 1-2
DOI:
https://doi.org/10.1556/sscmath.40.2003.1-2.20
Authors:
G. Kéri
and
P. R. J. Östergård

The minimum number of codewords in a code with t ternary and b binary coordinates and covering radius R is denoted by K(t,b,R). In this paper, necessary and sufficient conditions for K(t,b,R)=M are given for all M = 5. By the help of generalized s-surjective codes, we develop new methods for finding bounds for K(t,b,R). These results are used to prove the equality K(9,0,5)=6 as well as some new lower bounds such as K(2,7,3) =7,  K(3,6,3)=8,  K(5,3,3)=8, and K(9,0,4)=9. Some bounds for (nonmixed) quaternary codes are also obtained.

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