欧拉图中的欧拉进动力系统与路数
The Euler adic dynamical system and path counts in the Euler graph
摘要：
给出了广义欧拉数的一个公式，证明了欧拉数的某些比值序列的单调性，并应用这些结果得到了一个新的证明：基于欧拉图的Bratteli-Vershik动力系统的自然对称测度是唯一的全支撑不变遍历Borel概率测度.证明的关键成分是一个二维的归纳论点和一对一的对应关系之间的大多数路径从两个顶点在同一级别的另一个顶点。
英文摘要：
We give a formula for generalized Eulerian numbers, prove monotonicity of sequences of certain ratios of the Eulerian numbers, and apply these results to obtain a new proof that the natural symmetric measure for the Bratteli-Vershik dynamical system based on the Euler graph is the unique fully supported invariant ergodic Borel probability measure. Key ingredients of the proof are a two-dimensional induction argument and a one-to-one correspondence between most paths from two vertices at the same level to another vertex.
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