In dense k-uniform hypergraphs with minimum codegree δn (δ>1/2), the number of tight Hamilton cycles satisfies log Ψ(G) ≥ k h(G) - n log binom(n,k-1) + n log n - n log e - o(n), where h(G) is the hypergraph entropy from fractional matchings.
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Counting tight Hamilton cycles in Dirac hypergraphs
In dense k-uniform hypergraphs with minimum codegree δn (δ>1/2), the number of tight Hamilton cycles satisfies log Ψ(G) ≥ k h(G) - n log binom(n,k-1) + n log n - n log e - o(n), where h(G) is the hypergraph entropy from fractional matchings.