Consider the following function:
set of vectors P.
// this set P is global and empty
 
void f(set S, vector v){
    if(S is empty){
        insert v into P;
        return;
    }
    for( i = n to 1 ){
        if( i in S ){
            v.push_at_back(i);
            // append
            f(S\{i} , v); // S\{i} is S after removing i
            v.pop_from_back();
            // erase last element
        }
    }
}

The function is called with the following values of S, v

S = {1, 2, 3, ..., n}