The asymptotics of the partition of the cube into Weyl simplices, and an encoding of a Bernoulli scheme

Abstract

We suggest a combinatorial method of encoding continuous symbolic dynamical systems. A~continuous phase space, the infinite-dimensional cube, turns into the path space of a tree, and the shift is mapped to a transformation which was called a "transfer." The central problem is that of distinguishability: does the encoding separate almost all points of the space? The main result says that the partition of the cube into Weyl simplices satisfies this property.\footnote{{\it Keywords:} combinatorial encoding, transfer, Bernoulli scheme, graded graph.