In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of digits. By converting a number less than n! to factorial representation, one obtains a sequence of n digits that can be converted to a permutation of n in a straightforward way, either using them as Lehmer code or as inversion table representation; in the former case the resulting map from integers to permutations of n lists them in lexicographical order. General mixed radix systems were studied by Georg Cantor. The term "factorial number system" is used by Knuth, while the French equivalent "numération factorielle" was first used in 1888. The term "factoradic", which is a portmanteau of factorial and mixed radix, appears to be of more recent date.
Read more about Factorial Number System: Definition, Examples, Permutations, Fractional Values
Famous quotes containing the words number and/or system:
“No Government can be long secure without a formidable Opposition. It reduces their supporters to that tractable number which can be managed by the joint influences of fruition and hope. It offers vengeance to the discontented, and distinction to the ambitious; and employs the energies of aspiring spirits, who otherwise may prove traitors in a division or assassins in a debate.”
—Benjamin Disraeli (1804–1881)
“... in America ... children are instructed in the virtues of the system they live under, as though history had achieved a happy ending in American civics.”
—Mary McCarthy (1912–1989)