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PreprintarXiv licencearXiv

The uniform Turán density of the tetrahedron

  • Matija Bucić
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Abstract

We prove that the uniform Turán density of K4(3) is equal to 1/2. Kielak, Král', Lamaison, Liu, Shu, and Wu have recently proved the same result using combinatorial methods, while our proof is Fourier-analytic. This result answers a question of Erdős and Sós from the founding 1982 paper on this topic.

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Cite

BibTeXRIS
BibTeX
@misc{bucic2026uniform,
  title = {{The uniform Turán density of the tetrahedron}},
  author = {Matija Bucić},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11802},
  eprint = {2609.11802},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11802},
}
RIS
TY  - UNPB
TI  - The uniform Turán density of the tetrahedron
AU  - Matija Bucić
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.11802
UR  - https://arxiv.org/abs/2609.11802
AB  - We prove that the uniform Turán density of K_4^(3) is equal to 1/2. Kielak, Král', Lamaison, Liu, Shu, and Wu have recently proved the same result using combinatorial methods, while our proof is Fourier-analytic. This result answers a question of Erdős and Sós from the founding 1982 paper on this topic.
ER  -