A graceful permutation on letters is a permutation such
For example, there are four graceful permutations on : , , , and . The number of graceful permutations on letters for , 2, ... are 1, 2, 4, 4, 8, 24, 32, 40, ... (OEIS A006967).
See alsoGraceful Graph
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ReferencesSloane, N. J. A. Sequence A006967/M3229 in "The On-Line Encyclopedia of Integer Sequences."Wilf, H.
"On Crossing Numbers, and Some Unsolved Problems." In Combinatorics,
Geometry, and Probability: A Tribute to Paul Erdős. Papers from the Conference
in Honor of Erdős' 80th Birthday Held at Trinity College, Cambridge, March 1993
(Ed. B. Bollobás and A. Thomason). Cambridge, England: Cambridge
University Press, pp. 557-562, 1997.Wilf, H. S. and Yoshimura,
N. "Ranking Rooted Trees and a Graceful Application." In Discrete
Algorithms and Complexity (Proceedings of the Japan-US Joint Seminar June 4-6, 1986,
Kyoto, Japan) (Ed. D. Johnson, T. Nishizeki, A. Nozaki and
H. S. Wilf). Boston, MA: Academic Press, pp. 341-350, 1987.
on Wolfram|AlphaGraceful Permutation
Cite this as:
Weisstein, Eric W. "Graceful Permutation."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GracefulPermutation.html