Ordered partitions

func part(_,    {.is_empty}) { [[]] }
func partitions({.is_empty}) { [[]] }
 
func part(s, args) {
  gather {
    s.combinations(args[0], { |*c|
      part(s - c, args.slice(1)).each{|r| take([c] + r) }
    })
  }
}
 
func partitions(args) {
  part(@(1..args.sum), args)
}
 
[[],[0,0,0],[1,1,1],[2,0,2]].each { |test_case|
  say "partitions #{test_case}:"
  partitions(test_case).each{|part| say part }
  print "\n"
}

Output:

partitions []:
[]

partitions [0, 0, 0]:
[[], [], []]

partitions [1, 1, 1]:
[[1], [2], [3]]
[[1], [3], [2]]
[[2], [1], [3]]
[[2], [3], [1]]
[[3], [1], [2]]
[[3], [2], [1]]

partitions [2, 0, 2]:
[[1, 2], [], [3, 4]]
[[1, 3], [], [2, 4]]
[[1, 4], [], [2, 3]]
[[2, 3], [], [1, 4]]
[[2, 4], [], [1, 3]]
[[3, 4], [], [1, 2]]