Odd-Sunflowers

Autor: Frankl, Peter, Pach, János, Pálvölgyi, Dömötör
Rok vydání: 2023
Předmět:
Druh dokumentu: Working Paper
Popis: 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--Szemer\'edi conjecture, recently proved by Naslund and Sawin, that there is a constant $\mu<2$ such that every family of subsets of an $n$-element set that contains no odd-sunflower consists of at most $\mu^n$ sets. We construct such families of size at least $1.5021^n$. We also characterize minimal odd-sunflowers of triples.
Databáze: arXiv