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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
##### Keywords:
graceful $$n$$-permutations; enumeration