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Improved Sidorenko bound for hypergraph Turan densities
Abstract
For every fixed integer r≥3, we prove that the Turán density of every r-uniform hypergraph F with m≥1 edges satisfies π(F)≤1−crm−(r−1)/r, where cr>0 depends only on r. This improves Sidorenko's general bound, whose gap from $1$ is of order m−1. Complete r-uniform hypergraphs show that the exponent (r−1)/r is optimal. The proof combines a potential argument for partial embeddings with the Lovász Local Lemma.
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BibTeX
@misc{chen2026improved,
title = {{Improved Sidorenko bound for hypergraph Turan densities}},
author = {Shuyan Chen and Xinmin Hou and Xizhi Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18944},
eprint = {2610.18944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18944},
}
RIS
TY - UNPB
TI - Improved Sidorenko bound for hypergraph Turan densities
AU - Shuyan Chen
AU - Xinmin Hou
AU - Xizhi Liu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18944
UR - https://arxiv.org/abs/2610.18944
AB - For every fixed integer r≥3, we prove that the Turán density of every r-uniform hypergraph F with m≥1 edges satisfies π(F)≤1−c_rm^−(r−1)/r, where c_r>0 depends only on r. This improves Sidorenko's general bound, whose gap from $1$ is of order m^−1. Complete r-uniform hypergraphs show that the exponent (r−1)/r is optimal. The proof combines a potential argument for partial embeddings with the Lovász Local Lemma.
ER -