Odd-sunflowers

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 Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant μ...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 206; p. 105889
Main Authors Frankl, Peter, Pach, János, Pálvölgyi, Dömötör
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2024
Subjects
Parity argument
Set systems
Sunflowers
Parity argument
Sunflowers
Set systems
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ISSN0097-3165
1096-0899
1096-0899
DOI10.1016/j.jcta.2024.105889

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Summary: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 Erdős–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 μn sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples.
ISSN:0097-3165
1096-0899
1096-0899
DOI:10.1016/j.jcta.2024.105889