@article{a372cd42b03141c7ae5f2c627848af9c,
title = "SUMSETS IN THE HYPERCUBE",
abstract = "A subset S of the Boolean hypercube \BbbFn2 is a sumset if S = A + A = \{a + b | a, b \in A\} for some A \subseteq \BbbFn2 . We prove that the number of sumsets in \BbbFn2 is asymptotically (2n - 1)22n-1 . Furthermore, we show that the family of sumsets in \BbbFn2 is almost identical to the family of all subsets of \BbbFn2 that contain a complete linear subspace of codimension 1.",
keywords = "additive combinatorics, combinatorics, sumsets",
author = "Noga Alon and Zamir, {O. R.}",
note = "Publisher Copyright: 314 Copyright {\textcopyright} by SIAM. Unauthorized reproduction of this article is prohibited. functions f and g denotes that f = (1 + o(1))g, where the o(1)-term tends to 0 as the parameters of the functions grow to infinity. Equivalently, this means that the limit of the ratio f/g as the parameters grow is 1.",
year = "2025",
doi = "10.1137/24M165569X",
language = "אנגלית",
volume = "39",
pages = "314--326",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",
}