A368830 -id:A368830 - cp's OEIS frontend

A368943 Number of unlabeled mappings from n points to themselves with unique square root (endofunctions).

1, 1, 1, 1, 3, 7, 11, 23, 50

Offset: 0

Keith J. Bauer, Jan 11 2024

A mapping f has a unique square root if there exists a unique g such that gg = f.

Two mappings (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.)

			For n = 4, representatives of the a(4) = 3 mappings up to relabeling are
  1->1 2->1 3->2 4->1
  1->2 2->3 3->1 4->1
  1->2 2->3 3->1 4->4
whose unique square roots are respectively
  1->1 2->1 3->4 4->2
  1->3 2->1 3->2 4->2
  1->3 2->1 3->2 4->4

Keith J. Bauer, Visualization of a(6)

The labeled version is A368867.

Cf. A000700 (permutations only) < this sequence < A368830 (any square maps) < A001372 (all maps).

a(8) from Andrew Howroyd, Jan 10 2024

A368858 Number of perfect cube unlabeled endofunctions from n points to themselves.

Original entry on oeis.org

1, 1, 3, 5, 12, 22, 49, 99

Offset: 0

Keith J. Bauer, Jan 08 2024

The same as A368830 but perfect cubes instead of perfect squares.

Cf. A001372, A163859 (labeled version).

cp's OEIS Frontend

A368943 Number of unlabeled mappings from n points to themselves with unique square root (endofunctions).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs