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- W2052017002 abstract "Let be the minimum number of parts of smaller diameter into which one can partition an arbitrary bounded subset of -dimensional Euclidean space . In 1933, Borsuk conjectured that . Recent results of Kahn-Kalai, Nilli, and the present author demonstrate that the class of integral polytopes is one of the most important classes having a direct connection with Borsuk's conjecture and problems close to it.In the present paper, with the use of the methods of the set-covering problem new upper bounds are obtained for the minimum number of parts of smaller diameter into which each -dimensional (0,1)-polytope or cross-polytope can be partitioned. These bounds are substantially better than the author's similar former results as well as all previously known bounds for .In addition, (0,1)-polytopes and cross-polytopes in small dimensions are studied in this paper." @default.
- W2052017002 created "2016-06-24" @default.
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- W2052017002 date "2002-10-31" @default.
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- W2052017002 title "The Borsuk problem for integral polytopes" @default.
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- W2052017002 doi "https://doi.org/10.1070/sm2002v193n10abeh000688" @default.
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