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Packing Convex Bodies by Cylinders
In Bezdek and Litvak (J Geom Anal 19:233–243, 2009 ) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993, 1951 ) we obtained a lower bound for the sum of relevant measures of cylinders covering a given d -dimensional convex body. In this paper we provide the packing counterp...
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| Published in: | Discrete & computational geometry 2016-04, Vol.55 (3), p.725-738 |
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| cites | cdi_FETCH-LOGICAL-c349t-d131837a17110b5ffad1d7e1d2a3f76d6962f2113e63541c1ae123b24a5fb44c3 |
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| container_title | Discrete & computational geometry |
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| creator | Bezdek, Károly Litvak, Alexander E. |
| description | In Bezdek and Litvak (J Geom Anal 19:233–243,
2009
) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993,
1951
) we obtained a lower bound for the sum of relevant measures of cylinders covering a given
d
-dimensional convex body. In this paper we provide the packing counterpart of these estimates. We also extend bounds to the case of
r
-fold covering and packing and show a packing analog of Falconer’s results (Math Proc Camb Philos Soc 87:81–96,
1980
). |
| doi_str_mv | 10.1007/s00454-016-9760-z |
| format | article |
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2009
) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993,
1951
) we obtained a lower bound for the sum of relevant measures of cylinders covering a given
d
-dimensional convex body. In this paper we provide the packing counterpart of these estimates. We also extend bounds to the case of
r
-fold covering and packing and show a packing analog of Falconer’s results (Math Proc Camb Philos Soc 87:81–96,
1980
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2009
) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993,
1951
) we obtained a lower bound for the sum of relevant measures of cylinders covering a given
d
-dimensional convex body. In this paper we provide the packing counterpart of these estimates. We also extend bounds to the case of
r
-fold covering and packing and show a packing analog of Falconer’s results (Math Proc Camb Philos Soc 87:81–96,
1980
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2009
) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993,
1951
) we obtained a lower bound for the sum of relevant measures of cylinders covering a given
d
-dimensional convex body. In this paper we provide the packing counterpart of these estimates. We also extend bounds to the case of
r
-fold covering and packing and show a packing analog of Falconer’s results (Math Proc Camb Philos Soc 87:81–96,
1980
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| fulltext | fulltext |
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| ispartof | Discrete & computational geometry, 2016-04, Vol.55 (3), p.725-738 |
| issn | 0179-5376 1432-0444 |
| language | eng |
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| source | Springer Nature |
| subjects | Banach spaces Combinatorics Computational geometry Computational Mathematics and Numerical Analysis Covering Cylinders Estimates Geometry Lower bounds Mathematics Mathematics and Statistics |
| title | Packing Convex Bodies by Cylinders |
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