factorial
Speech parts
1. factorial - Noun
2. factorial - Adjective
Meaning
Of or pertaining to a factory.
Related to factorials.
A name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x).F(x + h).F(x + 2h) . . . F[x + (n-1)h] is called a factorial term, and its several factors take the name of factorials.
The product of the consecutive numbers from unity up to any given number.
Source: Webster's dictionarySynonyms
Hypernyms
Phrases with the word
Examples
1, 2, 6, 24, and 120 are factorials
Although Euler was a pioneer in the theory of complex variables, he does not appear to have considered the factorial of a complex number, as instead Gauss first did.
A more restrictive property than satisfying the above interpolation is to satisfy the recurrence relation defining a translated version of the factorial function, : for x equal to any positive real number.
An obvious way to generate permutations of n is to generate values for the Lehmer code (possibly using the factorial number system representation of integers up to n!), and convert those into the corresponding permutations.
Even for ordinary permutations it is significantly more efficient than generating values for the Lehmer code in lexicographic order (possibly using the factorial number system ) and converting those to permutations.
A passcode of four digits, if the four digits in question are known, is reduced from 10,000 possibilities to just 24 possibilities (10 4 versus 4! ( factorial of 4)).