A060135 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.

1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 1, 2, 1

Offset: 0

Author

Antti Karttunen, Mar 02 2001

Keywords

• nonn

Comments

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.

Links

• A. Karttunen, Truncated octahedron
• Index entries for sequences related to bell ringing

Crossrefs

Cf. A057112.

Programs

Maple

sol9seq := n -> (`if`((n < 13),adj_tp_seq(n), sol9seq(24-n)));

Formula

[seq(sol9seq(n), n=1..23)];