A061545
Number of pair-exchange / set-rotate sequences achieving the minimum length of A048200(n).
Original entry on oeis.org
0, 2, 1, 1, 1, 2, 4, 16, 40, 512, 1472, 65536, 208896
Offset: 1
Let "r" denote rotation and "x" an exchange.
For n = 5, the shortest sequence reversing "ABCDE" has length A048200(5) = 10, the only sequence doing so is "xrrxrrxrxr", so a(5) = 1.
For n = 6, we have A048200(6) = 15, but there are 2 solutions of this length "xrxrrxrxrrxrrrx" and "rxrrxrxrrxrxrrx", so a(6) = 2.
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Original entry on oeis.org
0, 1, 3, 7, 17, 32, 55, 87, 129, 184, 251
Offset: 1
a(5) = 0 + 1 + 2 + 4 + 10 = 17 is prime.
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).
Original entry on oeis.org
0, 1, 2, 4, 8, 13, 19, 26, 34, 43, 53, 64, 76
Offset: 1
- Danilo Bazzanella, Antonio Di Scala, Simone Dutto, and Nadir Murru, Primality tests, linear recurrent sequences and the Pell equation, arXiv:2002.08062 [math.NT], 2020.
- Sai Satwik Kuppili, C++ program for generating the moves for a given n
- Sai Satwik Kuppili and Bhadrachalam Chitturi, An Upper Bound for Sorting R_n with LRE, arXiv:2002.07342 [cs.DS], 2020.
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def a186752(n): t = tuple(1..n); G = PermutationGroup([[(1, 2)], [t], PermutationGroupElement([t])^(-1)]); return G.cayley_graph().distance(G.one(),G(list(t)[::-1])) # Max Alekseyev, Sep 09 2011
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