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PreprintCC BY 4.0arXiv

Three-Layer Intersecting Temperate Families

  • Kada Williams
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Abstract

In response to a conjecture of Petr and Turek, we prove that every largest intersecting temperate collection of sets 𝒜⊆ [2k](k)∪ [2k](k+1)∪ [2k](k+2) includes all k-sets containing some given a∈[2k], all (k+1)-sets, and all (k+2)-sets not containing a.

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Cite

BibTeXRIS
BibTeX
@misc{williams2026threelayer,
  title = {{Three-Layer Intersecting Temperate Families}},
  author = {Kada Williams},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24747},
  eprint = {2609.24747},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24747},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Three-Layer Intersecting Temperate Families
AU  - Kada Williams
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24747
UR  - https://arxiv.org/abs/2609.24747
AB  - In response to a conjecture of Petr and Turek, we prove that every largest intersecting temperate collection of sets 𝒜⊆ [2k]^(k)∪ [2k]^(k+1)∪ [2k]^(k+2) includes all k-sets containing some given a∈[2k], all (k+1)-sets, and all (k+2)-sets not containing a.
ER  -