Odd-Sunflowers
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917618752946176 |
|---|---|
| author | Frankl, Peter Pach, János Pálvölgyi, Dömötör |
| author_facet | Frankl, Peter Pach, János Pálvölgyi, Dömötör |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Odd-Sunflowers Frankl, Peter Pach, János Pálvölgyi, Dömötör Combinatorics 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. |
| title | Odd-Sunflowers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2310.16701 |