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Efficient enumeration of graceful permutations. (English) Zbl 1297.05007
Summary: A graceful \(n\)-permutation is a graceful labeling of an \(n\)-vertex path \(P_n\). In this paper we improve the asymptotic lower bound on the number of such permutations from \(\Omega ((5/3)^n)\) to \(\Omega(2.37^n)\). This is a computer-assisted proof based on an effective algorithm that enumerates graceful \(n\)-permutations. Our algorithm is also presented in detail.

MSC:
05A05 Permutations, words, matrices
05A15 Exact enumeration problems, generating functions
05C38 Paths and cycles
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