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arXiv · 2310.16701

Odd-Sunflowers

Peter Frankl·János Pach·Dömötör Pálvölgyi
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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.

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BibTeXRIS

Peter Frankl, János Pach, Dömötör Pálvölgyi. 2024-03-20. Odd-Sunflowers. https://arxiv.org/abs/2310.16701

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