The factorial number system, also known as the factoradic number system or Lehmer code, is a mathematical numeral system that represents non-negative integers as a sequence of digits. It is based on the concept of factorials, which are the product of all positive integers less than or equal to a given number.
In the factorial number system, each digit position represents a factorial number, starting with 0 at the rightmost position. The value of each digit can range from 0 to the position number, indicating how many times the factorial number is included in the original number. The value of each position increases from right to left, following factorials in ascending order.
For example, the integer 10 can be represented in the factorial number system as 1010. This implies that there are 1 copy of 3! (6), 0 copies of 2! (2), 1 copy of 1! (1), and 0 copies of 0! (1). Thus, the decimal value of 1010 in the factorial number system is 6*3! + 0*2! + 1*1! + 0*0! = 18.
The factorial number system is primarily used in combinatorial mathematics, such as permutation problems. It provides a convenient way to represent and calculate with permutations and combinations, making it beneficial in various fields such as computer science, probability theory, and statistics.
