The Euler adic dynamical system and path counts in the Euler graph

Details The Euler adic dynamical system and path counts in the Euler graph The Euler adic dynamical system and path counts in the Euler graph

2008-11-11

arxiv.org/abs/0811.1733v4

Mathematics

Dynamical Systems

Couple of small changes, one reference added. To appear in Tokyo Journal of Mathematics

Scientific paper

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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