
COMMENTS

Also known as square maps or square mapping patterns.
Two endofunctions are taken to be equivalent up to labeling if one is the conjugation of the other by a permutation. (Conjugation is applying the inverse permutation, the endofunction, and then the permutation, in that order. This is equivalent to permuting the "labels" of the set.)


EXAMPLE

The a(3) = 4 square endofunctions are:
1>1, 2>2, 3>3
1>1, 2>1, 3>1 (equivalent to any constant function)
1>1, 2>2, 3>1 (equivalent to any function consisting of 2 1cycles)
1>2, 2>3, 3>1 (equivalent to any 3cycle)
Each function listed here is its own square root, except for the 3cycle, whose square root is its inverse.
