PreprintCC BY-NC-SA 4.0arXiv
An Improvement to the Upper Bound for Marton's Covering Conjecture
Abstract
Marton's covering conjecture studies finite sets in high-dimensional binary spaces whose pairwise sums create relatively few new elements. It predicts that every such set can be described efficiently by shifted copies of one linear subspace of comparable size. Gowers, Green, Manners, and Tao [GGMT25] proved the conjecture with exponent $12$. Liao [L24] improved the exponent to $9$. We improve it further to $5.287$.
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BibTeX
@misc{song2026improvement,
title = {{An Improvement to the Upper Bound for Marton's Covering Conjecture}},
author = {Zhao Song and Song Yue},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30336},
eprint = {2608.30336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30336},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - An Improvement to the Upper Bound for Marton's Covering Conjecture
AU - Zhao Song
AU - Song Yue
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2608.30336
UR - https://arxiv.org/abs/2608.30336
AB - Marton's covering conjecture studies finite sets in high-dimensional binary spaces whose pairwise sums create relatively few new elements. It predicts that every such set can be described efficiently by shifted copies of one linear subspace of comparable size. Gowers, Green, Manners, and Tao [GGMT25] proved the conjecture with exponent $12$. Liao [L24] improved the exponent to $9$. We improve it further to $5.287$.
ER -