A060135 - OEIS

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

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OFFSET

0,2

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

Table of n, a(n) for n=0..22.

A. Karttunen, Truncated octahedron

Index entries for sequences related to bell ringing

FORMULA