What is the number of idempotent functions ?

Advertisements

Skip to content
# It’s counting time

##
2 thoughts on “It’s counting time”

### Leave a Reply

What is the number of idempotent functions ?

Advertisements

%d bloggers like this:

It is relatively straightforward to prove that if is the number of such functions, then for , with . If is the EGF of such sequence of numbers, one obtains after some algebra that with initial condition , which gives , and hence a closed formula for the .

LikeLiked by 2 people

A low brow solution: an idempotent function is uniquely determined by its set of fixed points together with its restriction . Conversely, this set of data uniquely determines an idempotent function.

Therefore, .

LikeLike