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An exclamation mark before a number instead of after it.
Also known as: Subfactorial, Derangement number, Exclamation mark before a number
!n counts derangements — permutations leaving nothing in its original place — and it is written with the exclamation mark moved to the front. That is the only thing distinguishing it from the ordinary factorial, which makes it one of the few notations where position alone carries the entire meaning.
Denotes the subfactorial: the number of permutations of n objects that fix none of them.
Contexts: Mathematics
Is distinguished from the factorial purely by the exclamation mark preceding rather than following the number.
Contexts: Mathematics
Approaches n! divided by e, which is why roughly 37 per cent of all permutations are derangements regardless of size.
Contexts: Mathematics
An upright stroke above a dot, placed immediately before a numeral rather than after it.