Using Clojure to compute partitions of a set

partitions.clj

(defn expand-partition
  "Given a partition of size n and an element, generate n new
  partitions by adding `element` to each subset in turn."
  [partition element]
  (let [partition (vec partition)]
    (for [i (range (count partition))]
      (set (update-in partition [i] #(conj % element))))))

(defn partitions
  "Return all partitions of the set `X` into `n` non-empty subsets.
  When `n` is not specified, return all partitions of `X`"
  ([X n]
     (cond
      (< n 1)         '()
      (> n (count X)) '()
      (= n 1)         (list #{X})
      (= n (count X)) (list (set (map hash-set X)))
      :else           (let [x  (first X)
                            xs (disj X x)]
                        (lazy-cat (map (fn [p] (conj p #{x})) (partitions xs (dec n)))
                                  (mapcat (fn [p] (expand-partition p x)) (partitions xs n))))))
  ([X]
     (mapcat (partial partitions X) (range 1 (inc (count X))))))