For every fixed r≥3, every vertex-relabeling-invariant Boolean property of simple r-uniform hypergraphs on n vertices satisfies Var_p(f)≤C_r I_p(f)/(log n)^(r/(r−1)) for all 0<p<1, without requiring monotonicity.
For every fixed r≥3, every vertex-relabeling-invariant Boolean property of simple r-uniform hypergraphs on n vertices satisfies Var_p(f)≤C_r I_p(f)/(log n)^(r/(r−1)) for all 0<p<1, without requiring monotonicity.
For every fixed r≥3, every vertex-relabeling-invariant Boolean property of simple r-uniform hypergraphs on n vertices satisfies Var_p(f)≤C_r I_p(f)/(log n)^(r/(r−1)) for all 0<p<1, without requiring monotonicity.
If correct, proves the hypergraph sharp-threshold width conjecture through a stronger nonmonotone influence inequality.
Do symmetric r-uniform hypergraph properties satisfy the conjectured influence and threshold-width bounds?
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OpenAI reports a uniform influence bound for hypergraph properties
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