Let E = K(n, m, D) be a Bedford-McMullen carpet with expanding factors n, m and digit set D. We call a = (aj)m-1 j=0 the distribution sequence of D where aj = #{i; (i, j) & ISIN; D}. Under a certain vertical separation condition, Li et al. (2013) [7] showed that if two totally disconnected Bedford-McMullent carpets share the same distribution sequence, then they are Lipschitz equivalent. In this paper, we define a metric & rho; on D & INFIN; and call (D & INFIN;, & rho;) a half-symbolic space. We show that if E is totally disconnected and satisfies the vertical separation condition, then E is ...
