On series of signed vectors and their rearrangements |
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Authors: | Wojciech Banaszczyk |
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Institution: | Faculty of Mathematics and Computer Science, University of ?ód?, ?ód?, Poland |
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Abstract: | Let x1,…,xm∈ \input amssym $ \Bbb R$ n be a sequence of vectors with ∥xi∥2 ≤ 1 for all i. It is proved that there are signs ε1,…,εm = ±1 such that where C1, C2 are some numerical constants. It is also proved that there are signs ε,…,ε = ±1 and a permutation π of {1,…,m} such that where C′ is some other numerical constant. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 |
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Keywords: | balancing vectors Steinitz lemma rearrangements of series |
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