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# Covering a planar domain with sets of small diameter

Periodica Mathematica Hungarica
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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# Finite linear coverings of locally connected continua

Periodica Mathematica Hungarica
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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# A criterion for finite lattice coverings

Periodica Mathematica Hungarica
Authors: Uwe Schnell and Achill Schürmann
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# On the covering radius of small codes

Studia Scientiarum Mathematicarum Hungarica
Authors: G. Kéri and P. R. J. Östergård

43 Östergård, P. R. J. And Blass, U., On the size of optimal binary codes of length 9 and covering radius 1, IEEE Trans. Inform. Theory 47 (2001), 2556-2557. MR 2002i :94092

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# Translative covering a convex body by its homothetic copies

Studia Scientiarum Mathematicarum Hungarica
Author: Janusz Januszewski

Lassak, M., Covering a plane convex body by four homothetical copies with the smallest positive ratio, Geom. Dedicata 21 (1986), 157-167. MR 88c :52013 Covering a plane convex body by

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# On small covering codes in arbitrary mixed hamming spaces

Studia Scientiarum Mathematicarum Hungarica
Author: Gerzson Kéri

Bertolo, R., Östergård, P. R. J. and Weakley, W. D. , An updated table of binary/ternary mixed covering codes, J. Combin. Des. 12 (2004), 157–176. MR 2005a :94086

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# On G-covering subgroup systems of finite groups

Acta Mathematica Hungarica
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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# Parallel packing and covering of an equilateral triangle with sequences of squares

Acta Mathematica Hungarica
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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# Fibrewise covering uniformities and completions

Acta Mathematica Hungarica
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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# Enumeration of branched coverings of closed orientable surfaces whose branch orders coincide with multiplicity

Studia Scientiarum Mathematicarum Hungarica
Authors: Jin Kwak and Alexander Mednykh

coverings of low-dimensional manifolds, Trans. Amer. Math. Soc. 247 (1979), 87–124. MR 80b :57003 Edmonds A. L. On the construction of branched coverings of low

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