Helpful combinatoric functions for Clojure

combinatorics.clj

(defn powerset [[h & t]]
  (if (nil? h)
    [()]
    (for [x (powerset t)
          y [x (cons h x)]]
      y)))

(defn tails [[ _ & t :as xs]]
  (when xs (cons xs (tails t))))

(defn k-combinations [k l]
  (if (zero? k)
    [[]]
    (for [[x & xs] (tails (seq l))
          ys (k-combinations (dec k) xs)]
      (cons x ys))))

(defn combinations [& [hs & tss]]
  (if (empty? hs)
    [[]]
    (for [h hs
          ts (apply combinations tss)]
      (cons h ts))))

(defn distribute [e [h & t :as xs]]
  (if (empty? xs)
    [[e]]
    (cons (cons e xs)
          (map #(cons h %) (distribute e t)))))

(defn permutations [xs]
  (if-let [[e & t] xs]
    (mapcat #(distribute e %) (permutations t))
    [[]]))