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A060135
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Sequence of adjacent transpositions (a[n] a[n]+1), which, when starting from the identity permutation and applied successively, produce a Hamiltonian circuit through all permutations of S_4, in such a way that S_{n-1} is always traversed before the rest of S_n. Furthermore, each subsequence from the first to the (n!-1)-th term is palindromic.
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2
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1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 1, 2, 1
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OFFSET
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0,2
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COMMENTS
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This is lexicographically the ninth of all such Hamiltonian paths through S4.
I will try to extend this in some elegant fashion through all S_inf so that the same criteria will hold. There are 466 ways to extend this to S5.
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LINKS
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FORMULA
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[seq(sol9seq(n), n=1..23)];
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MAPLE
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sol9seq := n -> (`if`((n < 13), adj_tp_seq(n), sol9seq(24-n)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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