|
|
A190141
|
|
The number of conjugacy classes of the symmetric group S_{0..n-1}, containing at least one complete bijection.
|
|
0
|
|
|
2, 4, 5, 8, 10, 18, 22, 34, 41, 63, 77, 111, 135, 190, 231
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|