PreprintCC BY 4.0arXiv
Counting sets with given doubling via dimension
Abstract
We determine, up to a factor of 2o(k), the number of k-sets A ⊂ {1, …, n} such that |A + A| ≤ m, where k = Θ(log n) and m ≤ k1 + α, for small α> 0, answering a question of Green and Morris.
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BibTeX
@misc{campos2026counting,
title = {{Counting sets with given doubling via dimension}},
author = {Marcelo Campos and Gabriel Dahia and João Pedro Marciano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05384},
eprint = {2609.05384},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05384},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Counting sets with given doubling via dimension
AU - Marcelo Campos
AU - Gabriel Dahia
AU - João Pedro Marciano
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.05384
UR - https://arxiv.org/abs/2609.05384
AB - We determine, up to a factor of 2^o(k), the number of k-sets A ⊂ {1, …, n} such that |A + A| ≤ m, where k = Θ(log n) and m ≤ k^1 + α, for small α> 0, answering a question of Green and Morris.
ER -