Bratteli图II上的完美序：一般Bratteli图
Perfect orderings on Bratteli diagrams II: general Bratteli diagrams
摘要：
我们继续我们的研究顺序Bratteli图开始在以前的工作中，与扬Kwiatkowski，在有限秩的Bratteli图被认为是联合。我们扩展的概念的语言，排列（在本文中称为对应），骨架和相关的图形的情况下，一般Bratteli图，并显示其相关性的研究完美的排序：那些支持Vershik地图，特别是完美的排序与几个极值路径。一个完美的排序配备了一个骨架和一个对应，相反，给定一个骨架和对应，我们明确地描述了如何构建完美的排序，通过显示相关的有向图中的路径确定的语言的顺序。我们描述了一个明确的算法方法来创建完美的排序Bratteli图的基础上的研究图的关联矩阵的条目和相关的图形的属性之间的某些关系，后者的关系特征图，支持完美的排序。此外，我们应用骨架和相关的图形的概念，给一个新的组合证明的事实，即图支持完美的排序与k个最大路径有一个直和的k-1副本的整数包含在其无穷小子群。在一定的条件下，我们证明了一个类似的结果持有，如果图支持可数多个极大路径。我们的结果说明了大量的例子。
英文摘要：
We continue our study of orderings on Bratteli diagrams started in previous work, joint with Jan Kwiatkowski, where Bratteli diagrams of finite rank were considered. We extend the notions of languages, permutations (called correspondences in this paper), skeletons and associated graphs to the case of general Bratteli diagrams, and show their relevance to the study of perfect orderings: those that support Vershik maps; in particular, perfect orderings with several extremal paths. A perfect ordering comes equipped with a skeleton and a correspondence, and conversely, given a skeleton and correspondence, we describe explicitly how to construct perfect orderings, by showing that paths in the associated directed graphs determine the language of the order. We describe an explicit algorithmic method to create perfect orderings on Bratteli diagrams based on the study of certain relations between the entries of the diagram's incidence matrices and properties of the associated graphs, with the latter relations characterizing diagrams which support perfect orderings. Also, we apply the notions of skeletons and associated graphs, to give a new combinatorial proof of the fact that diagrams supporting perfect orderings with k maximal paths have a direct sum of k-1 copies of the integers contained in their infinitesimal subgroup. Under certain conditions, we show that a similar result holds if the diagram supports countably many maximal paths. Our results are illustrated by numerous examples.
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