Permutations

cyclicPerms.js

// cyclicPerms(5)
//    "1,2,3,4,5
//    2,3,4,5,1
//    3,4,5,1,2
//    4,5,1,2,3
//    5,1,2,3,4" 
const cyclicPerms = (n) => 
    Array.from({length: n},(_,i) => i + 1)
    .map((_, i, xs) => [...xs, ...xs].slice(i, i+n))
    .join('\n')

perms.js

// To interleave x into an array is to return a list of all possible ways of inserting x into it.
// interleave("e")(["a", "r"]) => [["e", "a", "r"], ["a", "e", "r"], ["a", "r", "e"]] 
let interleave = (x) => ([y, ...ys]) => 
    y === undefined ? [[x]] :
    [[x, y, ...ys], ...interleave(x)(ys).map(i => [y, ...i])]

// returns all permutations of the array
// perms(['e','r','a']) => [["e", "r", "a"], ["r", "e", "a"], ["r", "a", "e"], ["e", "a", "r"], ["a", "e", "r"], ["a", "r", "e"]] 
let perms = ([x, ...xs]) => 
    x == undefined ? [[]] :
    perms(xs).map(interleave(x)).flatMap(t => t)