One-Dimensional Central Measures on Numberings of Ordered Sets

We describe one-dimensional central measures on numberings (tableaux) of ideals partially ordered sets (posets). As the main example, we study poset $$\mathbb{Z}_+^d$$ and graph its finite ideals, multidimensional Young tableaux; for $$d=2$$ , this is ordinary graph. The are stratified by dimension; in paper give a complete description stratum prove that every ergodic measure uniquely determined frequencies. suggested method, particular, gives first purely combinatorial proof E. Thoma’s theorem different from Plancherel (which dimension $$2$$ ).