Open Research Index

Improved Sidorenko bound for hypergraph Turán densities

Xizhi Liu

Palomar Registrypalomar/PALOMAR-2026-10-13-000012Oct 13, 2026math.COscore 0

For every finite simple r-uniform hypergraph F with r >= 3 and m >= 1 edges, the Turán density is at most 1-c_r/m^((r-1)/r), where c_r=(1/(4r^2))(4/r)^(1/r)(1-1/r)^(2-2/r). The formalization proves the finite embedding argument using two potentials and the Lovász Local Lemma, constructs the extremal numbers, and proves the existence of their binomial-normalized limit by vertex deletion and double counting.

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