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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Constructs even-dimensional Latin hypercubes of orders 4, 6, 8 and all even n >= 10 whose transversals are forced to hit specific (d-2)-planes or leave exponentially many cells uncovered.
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Entropy Bounds for Perfect Matchings in Bipartite Hypergraphs
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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Latin hypercubes with restricted transversals
Constructs even-dimensional Latin hypercubes of orders 4, 6, 8 and all even n >= 10 whose transversals are forced to hit specific (d-2)-planes or leave exponentially many cells uncovered.