1,3

Sizes of orbits are given by A000793.

For S={a}, n=1 and only one operation possible {a->a}. For S={a,b}, n=2 and possible operations are {a->a,b->a}, {a->a,b->b}, {a->b,b->a},{a->b,b->b}. Longest orbit generated by applying operation {a->b,b->a}: initial set (a,b), applying function gives orbit - (b,a), (a,b). All other possible functions are generating fixed points.

Sequence in context: A082690 A104861 A074859 this_sequence A103160 A126099 A063753

Adjacent sequences: A162679 A162680 A162681 this_sequence A162683 A162684 A162685

nonn

Dmitriy Samsonov (dmitriy.samsonov(AT)gmail.com), Jul 10 2009