Spectrum and absolute of the graph of two-row Young diagrams

For the simplest graph of two-rows Young diagrams we are giving the elementary presentation of the theory of the traces of $AF$-algebras and the central measures The implicit description of measures as Markov chains with two states is given. We emphasize the role of the notion of homogeneity in this context. We embedded the homogeneity central measures besides only one of them to the Bernoulli scheme and from the other side the isomorphism (RSK) of each of them with those schemes. We also give a geometrical condition of the centrality of the measure.