(42S) Subfactorial

[ijabbott]

(09-06-2021 04:43 PM)Eddie W. Shore Wrote:  The subfactorial finds all the possible arrangements of a set of objects where none of the objects end up in their original position.

For example, when arranging the set {1, 2, 3, 4} the subfactorial counts sets such as {2, 1, 4, 3} and {3, 4, 1, 2} but not {1, 4, 3, 2}. For the positive integers: !n < n!.

I believe such arrangements are called "derangements" in combinatorics, so the subfactorial is the number of derangements. Great word!