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.

%I #10 Jun 12 2021 23:34:57

%S 1,2,1,2,1,3,1,2,3,2,1,2,1,2,3,2,1,3,1,2,1,2,1

%N 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.

%C This is lexicographically the ninth of all such Hamiltonian paths through S4.

%C 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.

%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/permgraf/troctahe.htm">Truncated octahedron</a>

%H <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>

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

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

%Y Cf. A057112.

%K nonn

%O 0,2

%A _Antti Karttunen_, Mar 02 2001