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 A186752 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). 1
 0, 1, 2, 4, 8, 13, 19, 26, 34 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS PROG (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] CROSSREFS Sequence in context: A030058 A058329 A037380 * A030503 A084684 A011907 Adjacent sequences:  A186748 A186750 A186751 * A186753 A186754 A186755 KEYWORD nonn,more,hard AUTHOR Tony Bartoletti, Feb 26 2011 EXTENSIONS a(8)=26 added by Tony Bartoletti, Mar 12 2011 a(9) from Max Alekseyev, Sep 09 2011 STATUS approved

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