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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). 2
0, 1, 2, 4, 8, 13, 19, 26, 34, 43, 53 (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.
It was suggested that a(10) = 61, but this cannot be correct. It would conflict with A186783(10)=45, the diameter of the set under these same operations. We must have a(n) <= A186783(n) for all n. - Tony Bartoletti, Mar 08 2019
LINKS
Danilo Bazzanella, Antonio Di Scala, Simone Dutto, Nadir Murru, Primality tests, linear recurrent sequences and the Pell equation, arXiv:2002.08062 [math.NT], 2020.
Sai Satwik Kuppili, Bhadrachalam Chitturi, An Upper Bound for Sorting R_n with LRE, arXiv:2002.07342 [cs.DS], 2020.
PROG
(Sage) def A186752(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)) # Max Alekseyev, Sep 09 2011
CROSSREFS
Sequence in context: A058329 A037380 A328005 * A360512 A030503 A245094
KEYWORD
nonn,more,hard
AUTHOR
Tony Bartoletti, Feb 26 2011
EXTENSIONS
a(9) from Max Alekseyev, Sep 09 2011
Incorrect value for a(10) deleted by N. J. A. Sloane, Mar 09 2019
a(10) and a(11) added by Sai Satwik Kuppili, Bhadrachalam Chitturi, Mar 28 2019
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)