The Lehmer code maps between permutations and natural numbers. My question: Is a "nice" algorithm known for composing permutations directly in the factoradic form?
When the permutations commute, it looks like digits can be added in modular fashion. For example, $$1\,1\,1\,0_{!} \cdot 2\,1\,0\,0_{!} =3\,2\,1\,0_!.$$
But when they don't, something more is wanted.