Geodesic
Tomaszewski's problem on randomly signed sums, revisited
Ravi B. Boppana1 ; Harrie Hendriks2 ; Martien C.A. van Zuijlen2
1Massachusetts Institute of Technology
2Radboud University Nijmegen
The electronic journal of combinatorics, Tome 28 (2021) no. 2
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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 $0.427685$.
DOI : 10.37236/9497
Classification : 60E15, 60G50, 60C05, 05A20
Mots-clés : Tomaszewski's problem

Ravi B. Boppana  1   ; Harrie Hendriks  2   ; Martien C.A. van Zuijlen  2

1 Massachusetts Institute of Technology
2 Radboud University Nijmegen 
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     title = {Tomaszewski's problem on randomly signed sums, revisited},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {2},
     doi = {10.37236/9497},
     zbl = {1470.60066},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9497/}
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Ravi B. Boppana; Harrie Hendriks; Martien C.A. van Zuijlen. Tomaszewski's problem on randomly signed sums, revisited. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9497

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