map length (tiers :: [[ Set Nat ]])  =  [1,1,1,2,2,3,4,5,6,8,10,12,...]

length (list :: [ Set Nat ])  =  Infinity

allUnique (list :: [ Set Nat ])  =  True

ratioRepetitions (list :: [ Set Nat ])  =  0 % 1

tiers :: [Set Nat]  =
  [ [Set []]
  , [Set [0]]
  , [Set [1]]
  , [ Set [0,1]
    , Set [2]
    ]
  , [ Set [0,2]
    , Set [3]
    ]
  , [ Set [0,3]
    , Set [1,2]
    , Set [4]
    ]
  , [ Set [0,1,2]
    , Set [0,4]
    , Set [1,3]
    , Set [5]
    ]
  , [ Set [0,1,3]
    , Set [0,5]
    , Set [1,4]
    , Set [2,3]
    , Set [6]
    ]
  , [ Set [0,1,4]
    , Set [0,2,3]
    , Set [0,6]
    , Set [1,5]
    , Set [2,4]
    , Set [7]
    ]
  , [ Set [0,1,5]
    , Set [0,2,4]
    , Set [0,7]
    , Set [1,2,3]
    , Set [1,6]
    , Set [2,5]
    , Set [3,4]
    , Set [8]
    ]
  , [ Set [0,1,2,3]
    , Set [0,1,6]
    , Set [0,2,5]
    , Set [0,3,4]
    , Set [0,8]
    , Set [1,2,4]
    , Set [1,7]
    , Set [2,6]
    , Set [3,5]
    , Set [9]
    ]
  , [ Set [0,1,2,4]
    , Set [0,1,7]
    , Set [0,2,6]
    , Set [0,3,5]
    , Set [0,9]
    , Set [1,2,5]
    , Set [1,3,4]
    , Set [1,8]
    , Set [2,7]
    , Set [3,6]
    , Set [4,5]
    , Set [10]
    ]
  , ...
  ]