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PreprintCC BY 4.0arXiv

Sunflower-Free Uniform Families: Recursive Constructions and Explicit Bounds

  • Edward Axante
  • Cristian Budala
  • David Chitic
  • Bogdan Dumitru
  • Mihai Nacu
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Abstract

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≤ f(3,4)≤49, f(3,5)≤146, 153≤ f(3,6)≤255, 259≤ f(3,7)≤474, and 54≤ f(4,3)≤83. 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.

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Cite

BibTeXRIS
BibTeX
@misc{axante2026sunflowerfree,
  title = {{Sunflower-Free Uniform Families: Recursive Constructions and Explicit Bounds}},
  author = {Edward Axante and Cristian Budala and David Chitic and Bogdan Dumitru and Mihai Nacu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06175},
  eprint = {2609.06175},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06175},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sunflower-Free Uniform Families: Recursive Constructions and Explicit Bounds
AU  - Edward Axante
AU  - Cristian Budala
AU  - David Chitic
AU  - Bogdan Dumitru
AU  - Mihai Nacu
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.06175
UR  - https://arxiv.org/abs/2609.06175
AB  - 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≤ f(3,4)≤49, f(3,5)≤146, 153≤ f(3,6)≤255, 259≤ f(3,7)≤474, and 54≤ f(4,3)≤83. 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.
ER  -