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Entropy Bounds for Perfect Matchings in Bipartite Hypergraphs

math.CO · 2025-06-21 · unverdicted · novelty 7.0

Entropy-based upper bounds on A-perfect matchings in uniform bipartite hypergraphs with bounded codegree yield (n/e^{2.117})^n transversals for odd-order Latin squares with n ≡ 0 mod 3 and ((1+o(1))q/e^k)^{Dn/k} proper q-edge-colorings for k-uniform D-regular hypergraphs with q ≈ D and small codeg

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  • Entropy Bounds for Perfect Matchings in Bipartite Hypergraphs math.CO · 2025-06-21 · unverdicted · none · ref 1

    Entropy-based upper bounds on A-perfect matchings in uniform bipartite hypergraphs with bounded codegree yield (n/e^{2.117})^n transversals for odd-order Latin squares with n ≡ 0 mod 3 and ((1+o(1))q/e^k)^{Dn/k} proper q-edge-colorings for k-uniform D-regular hypergraphs with q ≈ D and small codeg