For example, it says "where {σ_1,...,σ_k} is the set of indexes of all possible subsets of {1,...,n}" instead of "where
{σ_1,..., σ_k} is a set of indexes taken from all possible different subsets of {1,...,n}". The difference between "the set ... of all possible" and "a set ... taken from all possible" would have been important here.