Algebraic Irrational Binary Numbers Cannot Be Fixed Points of Non-trivial Constant Length or Primitive Morphisms

@inproceedings{Allouche1998AlgebraicIB,
  title={Algebraic Irrational Binary Numbers Cannot Be Fixed Points of Non-trivial Constant Length or Primitive Morphisms},
  author={Jean-Paul Allouche and Luca Q. Zamboni},
  year={1998}
}
How random are the digits of an algebraic irrational number in a given base? A common conjectured answer to this vague question is that these digits are ``really random.'' For example, define a normal number in base k 2 to be a real number x such that, for each integer d 1, each block of length d occurs in the k-ary expansion of x with frequency 1 k. A widely believed conjecture is that an algebraic irrational number is a normal number in each base k 2. This conjecture is open and seems really… CONTINUE READING

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