A190141 - OEIS

%I #11 Jan 08 2013 08:53:26

%S 2,4,5,8,10,18,22,34,41,63,77,111,135,190,231

%N The number of conjugacy classes of the symmetric group S_{0..n-1}, containing at least one complete bijection.

%C X = {0..n-1}, and n >= 3. Suppose c is a cycle on X, with length L>1, and support C. Define a map e(c) : X --> X, by ec(x) = x for x not in C, and supposing x = ck, 0 <= k < L, we define ec(x) = cs, with s == ( k + ck) Mod L. If e(c) is a bijection on X, we call e(c) a complete bijection.

%e n = 6, a(6) = 5. We have:

%e e((1->3->5->2->4)) = (1->3->4->5), ec((0->3->1->4->2)) = (1->4)(2->3),

%e ec((1->2->4->5)) = (1->2->5), ec((1->3)) = (1->3) and ec((0->2))= identity.

%e The remaining conjugacy classes don't contain a complete bijection.

%Y Cf. A003111

%K nonn,more

%O 3,1

%A _Bert Schaaf_, May 05 2011