The most elegant way to generate permutations in SQL server

Question

Given a the following table:

Index | Element
---------------
  1   |    A
  2   |    B
  3   |    C
  4   |    D

We want to generate all th

Answer 1

Am I correctly understanding that you built Cartesian product n x n x n x n, and then filter out unwanted stuff? The alternative would be generating all the numbers up to n! and then using factorial number system to map them via element encoding.