论文标题
一维中心措施对有序集的数量
One-dimensional central measures on numberings of ordered sets
论文作者
论文摘要
我们描述了部分有序集（POSETS）的编号（tableaux）的一维中心度量（tableaux）。作为主要示例，我们研究了poset $ {\ bbb z} _+^d $及其有限理想的图表，多维的年轻tableaux；对于$ d = 2 $，它是普通的年轻图。中央度量按维度分层；在本文中，我们对一维层进行了完整的描述，并证明每个厄贡中心度量都是由其频率唯一决定的。尤其是建议的方法给出了E.〜thoma定理的第一个纯粹的组合证明，用于一维中心度量与Plancherel量度不同（尺寸约为$ 2 $）。
We describe one-dimensional central measures on numberings (tableaux) of ideals of partially ordered sets (posets). As the main example, we study the poset ${\Bbb Z}_+^d$ and the graph of its finite ideals, multidimensional Young tableaux; for $d=2$, it is the ordinary Young graph. The central measures are stratified by dimension; in the paper we give a complete description of the one-dimensional stratum and prove that every ergodic central measure is uniquely determined by its frequencies. The suggested method, in particular, gives the first purely combinatorial proof of E.~Thoma's theorem for one-dimensional central measures different from the Plancherel measure (which is of dimension~$2$).
