A190141 The number of conjugacy classes of the symmetric group S_{0..n-1}, containing at least one complete bijection.

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

Offset: 3

Author

Bert Schaaf, May 05 2011

Keywords

• nonn
• more

Comments

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.

Examples

			n = 6, a(6) = 5. We have:
e((1->3->5->2->4)) = (1->3->4->5), ec((0->3->1->4->2)) = (1->4)(2->3),
ec((1->2->4->5)) = (1->2->5), ec((1->3)) = (1->3) and ec((0->2))= identity.
The remaining conjugacy classes don't contain a complete bijection.
		

Crossrefs

Cf. A003111