Tomaszewski's Problem on Randomly Signed sums, Revisited
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Published:2021-06-04
Issue:2
Volume:28
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Boppana Ravi B.,Hendriks Harrie,Van Zuijlen Martien C.A.
Abstract
Let $v_1,v_2,\ldots, v_n$ be real numbers whose squares add up to 1. Consider the $2^n$ signed sums of the form $S = \sum \pm v_i$. Boppana and Holzman (2017) proved that at least 13/32 of these sums satisfy $|S| \le 1$. Here we improve their bound to $0.427685$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics