Tomaszewski's problem on randomly signed sums, revisited
| Autor: | Boppana, Ravi B., Hendriks, Harrie, van Zuijlen, Martien C. A. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Electronic Journal of Combinatorics 28:2, #P2.35, 2021 |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $0.427685$. Comment: Now with three authors. 4 pages |
| Databáze: | arXiv |
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