Tomaszewski's problem on randomly signed sums, revisited

Tomaszewski's problem on randomly signed sums, revisited

Electronic Journal of Combinatorics 28:2, #P2.35, 2021 Let $v_1$, $v_2$, ..., $v_n$ 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...

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Hauptverfasser: Boppana, Ravi B, Hendriks, Harrie, van Zuijlen, Martien C. A
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Probability
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Zusammenfassung:Electronic Journal of Combinatorics 28:2, #P2.35, 2021 Let $v_1$, $v_2$, ..., $v_n$ 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 $0.427685$.
DOI:10.48550/arxiv.2003.06433