发表机构
Faculty of Mathematics and Computer Science, University of Bucharest（布加勒斯特大学数学与计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过递归构造和计算机辅助方法，给出了无向日葵一致族最大大小$f(w,k)$的上下界，并确定了特定情形下的精确值。
AI 中文摘要
设$f(w,k)$为不含$k$个花瓣的向日葵的$w$-一致族的最大大小。我们引入无向日葵族的递归构造，并利用它获得$f(w,k)$指数增长率的通用下界。我们还证明了至少具有四个花瓣的$3$-一致族的通用上界。我们的结果给出$39\le f(3,4)\le49$，$f(3,5)\le146$，$153\le f(3,6)\le255$，$259\le f(3,7)\le474$，以及$54\le f(4,3)\le83$。此外，我们证明不含三个花瓣的向日葵的交错$4$-一致族的最大大小为$27$。上界$49$和$83$是计算机辅助得到的。有限下界来自显式构造。
英文摘要
Let $f(w,k)$ be the maximum size of a $w$-uniform family containing no sunflower with $k$ petals. We introduce a recursive construction for sunflower-free families and use it to obtain a general lower bound on the exponential growth rate of $f(w,k)$. We also prove a general upper bound for $3$-uniform families with at least four petals. Our results give $39\le f(3,4)\le49$, $f(3,5)\le146$, $153\le f(3,6)\le255$, $259\le f(3,7)\le474$, and $54\le f(4,3)\le83$. In addition, we prove that the maximum size of an intersecting $4$-uniform family containing no sunflower with three petals is $27$. The upper bounds $49$ and $83$ are computer-assisted. The finite lower bounds come from explicit constructions.
