proposed

approved

editing

proposed

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.

approved

editing

_Antti Karttunen _, Mar 02 2001

<a href="/Sindx_index/Be.html#bell_ringing">Index entries for sequences related to bell ringing</a>

<a href="/Sindx_Be.html#bell_ringing">Index entries for sequences related to bell ringing</a>

nonn,new

nonn

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 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.

<a href="http://www.research.att.com/~njas/sequences/Sindx_Be.html#bell_ringing">Index entries for sequences related to bell ringing</a>

nonn,new

nonn

<a href="http://www.research.att.com/~njas/sequences/Sindx_Be.html#bell_ringing">Index entries for sequences related to bell ringing</a>

nonn,new

nonn

nonn,new

nonn

Antti Karttunen 05 Mar 02 2001

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 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

0,2

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.

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

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

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

Cf. A057112.

nonn

Antti Karttunen 05 Mar 2001

approved