Year: 2023
Type: preprint
Abstract: Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erd\H os--Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant $μ<2$ such that every family of subsets of an $n$-element set that contains no odd-sunflower consists of at most $μ^n$ sets. We construct such families of size at least $1.5021^n$. We also characterize minimal odd-sunflowers of triples.
Source: arXiv (Cornell University)
Authors: Frankl, Peter, Pach, János, Pálvölgyi, Dömötör
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387964096