The factorial number system is a type of positional notation in which the digits represent the factorials of successive integers. There are various synonyms for this term, such as the Factorial base system, Factoradic Number System, and Lehmer Code. The Factorial base system is a numeral system whose base is defined by factorials of integers. The Factoradic Number System is based on the factorial expansion of a number, where a sequence of digits represents the coefficients of the successive factorials that make up the number. Lehmer Code is a representation of a permutation of a set in the factorial base system, which is useful in combinatorics. These synonyms are often used interchangeably in mathematics and computer science.