Odd-sunflowers
Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889.
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Author
Frankl, Peter;
Pach, JánosISTA;
Pálvölgyi, Dömötör
Corresponding author has ISTA affiliation
Department
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 Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples.
Publishing Year
Date Published
2024-03-20
Journal Title
Journal of Combinatorial Theory, Series A
Publisher
Elsevier
Acknowledgement
We are grateful to Balázs Keszegh, and to the members of the Miklós Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib for pointing out several important mathematical typos.
Volume
206
Issue
8
Article Number
105889
ISSN
eISSN
IST-REx-ID
Cite this
Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 2024;206(8). doi:10.1016/j.jcta.2024.105889
Frankl, P., Pach, J., & Pálvölgyi, D. (2024). Odd-sunflowers. Journal of Combinatorial Theory, Series A. Elsevier. https://doi.org/10.1016/j.jcta.2024.105889
Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” Journal of Combinatorial Theory, Series A. Elsevier, 2024. https://doi.org/10.1016/j.jcta.2024.105889.
P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” Journal of Combinatorial Theory, Series A, vol. 206, no. 8. Elsevier, 2024.
Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889.
Frankl, Peter, et al. “Odd-Sunflowers.” Journal of Combinatorial Theory, Series A, vol. 206, no. 8, 105889, Elsevier, 2024, doi:10.1016/j.jcta.2024.105889.
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