Factoradic Converter
About the Factorial System (Factoradic)
The factorial number system is a mixed radix numeral system. A number is represented by a sequence of digits dₙ...d₂d₁d₀ where each digit dᵢ is a coefficient for the factorial i!.
The key constraint is that each digit dᵢ must satisfy 0 ≤ dᵢ ≤ i. This makes the system unambiguous. Its primary use is in combinatorics for indexing permutations.
Interactive Factoradic Builder
Use the controls to build a factoradic number. Each digit is constrained to its valid range. The decimal value updates automatically.
Permutation Tools
Factoradics provide a direct way to map an integer index to a unique permutation of a set of elements.
Generate N-th Permutation
Find Permutation Rank
Factorial Reference
Factorials and their Digits
In the factoradic system ...d₂d₁d₀, the digit dᵢ must be between 0 and i inclusive. The maximum number of permutations for a set of size N is N!, which means the valid indices are 0 to N! - 1.
| n | n! (Value) | Max digit dₙ | Total Permutations |
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