Geodesic
Anticoncentration versus the number of subset sums
Advances in Combinatorics (2021) Cet article a éte moissonné depuis la source Scholastica

Voir la notice de l'article

Let $\vec{w} = (w_1,\dots, w_n) \in \mathbb{R}^{n}$. We show that for any $n^{-2}\leε\le 1$, if \[\#\{\vecξ \in \{0,1\}^{n}: \langle \vecξ, \vec{w} \rangle = τ\} \ge 2^{-εn}\cdot 2^{n}\] for some $τ\in \mathbb{R}$, then \[\#\{\langle \vecξ, \vec{w} \rangle : \vecξ \in \{0,1\}^{n}\} \le 2^{O(\sqrtεn)}.\] This exponentially improves the $ε$ dependence in a recent result of Nederlof, Pawlewicz, Swennenhuis, and Węgrzycki and leads to a similar improvement in the parameterized (by the number of bins) runtime of bin packing.
Publié le : 
@article{ADVC_2021_a3,
     author = {Vishesh Jain and Ashwin Sah and Mehtaab Sawhney},
     title = {Anticoncentration versus the number of subset sums},
     journal = {Advances in Combinatorics},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a3/}
}
TY  - JOUR
AU  - Vishesh Jain
AU  - Ashwin Sah
AU  - Mehtaab Sawhney
TI  - Anticoncentration versus the number of subset sums
JO  - Advances in Combinatorics
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/ADVC_2021_a3/
LA  - en
ID  - ADVC_2021_a3
ER  - 
%0 Journal Article
%A Vishesh Jain
%A Ashwin Sah
%A Mehtaab Sawhney
%T Anticoncentration versus the number of subset sums
%J Advances in Combinatorics
%D 2021
%U http://geodesic.mathdoc.fr/item/ADVC_2021_a3/
%G en
%F ADVC_2021_a3
Vishesh Jain; Ashwin Sah; Mehtaab Sawhney. Anticoncentration versus the number of subset sums. Advances in Combinatorics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a3/