Moonflowers and efficient code sparsification
Combinatorics
2026-05-12 v1
Abstract
We introduce \emph{moonflowers}, a weaker analogue of sunflowers. A family of sets is a -moonflower if each set contains at least one element that is absent from all the others. We study the extremal problem of determining the largest possible size of a family of sets of size at most that avoids a -moonflower, and obtain near-optimal bounds. As an application, we revisit the code sparsification problem studied by Brakensiek and Guruswami (STOC 2025) and improve the bounds to near optimal. Concretely, we improve the dependence on the block length from poly-logarithmic to logarithmic, and show that such a dependence is necessary.
Cite
@article{arxiv.2605.08676,
title = {Moonflowers and efficient code sparsification},
author = {Shachar Lovett and Raghu Meka and Yimeng Wang},
journal= {arXiv preprint arXiv:2605.08676},
year = {2026}
}