Clarification of the Definition of Permutations

Question

In set theory, when defining the permutations of a given string, does the original string count as a permutation of itself?

I.e., would a set of the permutations of "stop" include:

{ stop, stpo, sotp, sopt, spto, spot, ... }

Furthermore, if any string is a permutation of itself, does that mean the relation 'is a permutation of' is reflexive?

Answer 1

I would say "Yes" to both questions: the original string is normally regarded as a permutation of itself, and hence the relation "is a permutation of" is reflexive.