F = factoradic(M,N) returns the conversion of integer M into factorial radix. F is a 1-by-N vector. The factoradic is also known as the Lehmer Code. The factoradic of M is best understood by example.
Example: 89 = 3x4! + 2x3! + 2x2! + 1x1! + 0x0!
therefore factoradic(89,5) = (3,2,2,1,0)
M must lie in the range [0 : N!-1].
Leading zeros will be present in F when M < (N-1)!-1.
Example: factoradic(19,6) = (0,0,3,0,1,0)
A practical use of the factoradic is the generation of permutations. See ONEPERM on the File Exchange.
Thanks to Stefano Bolli for noticing a typo in the error-checking.