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A186752
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Length of minimum representation of the permutation [n,n-1,...,1] as the product of transpositions (1,2) and left and right rotations (1,2,...,n).
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1
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OFFSET
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1,3
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COMMENTS
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Example: Taking "0" to indicate the "left" rotation (1,2,...,n) -> (2,3,...,n,1), "1" to represent the transposition (1,2), and "2" to indicate the "right" rotation (1,2,...,n) -> (n,1,2,...n-1), the sequence 10010121 (length = 8) is a minimal sequence producing the reverse permutation on S_5.
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LINKS
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Table of n, a(n) for n=1..9.
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PROG
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(SAGE) def a(n): t = tuple(1..n); G = PermutationGroup([[(1, 2)], [t], PermutationGroupElement([t])^(-1)]); t=list(t); t.reverse(); return G.cayley_graph().distance(G([()]), G(t)) # [From Max Alekseyev]
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CROSSREFS
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Sequence in context: A030058 A058329 A037380 * A030503 A084684 A011907
Adjacent sequences: A186748 A186750 A186751 * A186753 A186754 A186755
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KEYWORD
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nonn,more,hard
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AUTHOR
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Tony Bartoletti, Feb 26 2011
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EXTENSIONS
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a(8)=26 added by Tony Bartoletti, Mar 12 2011
a(9) from Max Alekseyev, Sep 09 2011
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STATUS
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approved
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