(M + 1)-step shift spaces that are not conjugate to M-step shift spaces
  Recently Ott, Tomforde and Willis proposed a new approach for one sided shift spaces over infinite alphabets. In this new approach the conjugacy classes of shifts of finite type, edge shifts, and M-step shifts are distinct and the authors conjecture that for each non-negative integer M there exist an (M+1)-step shift space that is not conjugate to any M-step shift. In this short paper we build a class of (M+1)-step shifts that are not conjugate to any M-step shift and hence show that their conjecture is correct. 
Daniel Gon\c{c}alves and Danilo Royer
math.DS math.GN math.OA