PowerSet.cs

// Generates partial permutations for a given string:
private HashSet<string> GeneratePartialPermutation(string word)
{
    return new HashSet<string>(Enumerable.Range(0, word.Length)
        .Select(i => word.Remove(i, 1).Insert(0, word[i].ToString())));
}

// Entry point for the recipe execution:
void Main()
{
    // Word with all characters to compute its power set:
    string word = "abc";

    // Create a set with the n-initial permutations:
    HashSet<string> perms = GeneratePartialPermutation(word);

    // Produces all the element pairs for each partial permutation
    // (e.g., for the word 'abc' there are three element pairs
    // {"a", "bc"}, {"ab", "c"}, {"abc"}:
    Enumerable.Range(0, word.Length)
        .ToList()
        .ForEach(x =>
            Enumerable.Range(0, word.Length)
                .ToList()
                .ForEach(z =>
                {
                    // First element pair:
                    perms.Add(perms.ElementAt(x).Substring(0, z));
                    // Second element pair:
                    perms.Add(perms.ElementAt(x).Substring(z+1));
                }));

    // Sorts and removes duplicates from all the generated element pairs:
    perms.Select(p => new string(p.ToCharArray()
        .OrderBy(x => x)
        .ToArray()))
        .Distinct()
        .OrderBy(p => p.Length)
        .Dump("Power set of 'abc'");
}