The Euler adic dynamical system and path counts in the Euler graph
Dynamical Systems
2009-09-21 v4 Combinatorics
Abstract
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.
Cite
@article{arxiv.0811.1733,
title = {The Euler adic dynamical system and path counts in the Euler graph},
author = {K. Petersen and A. Varchenko},
journal= {arXiv preprint arXiv:0811.1733},
year = {2009}
}
Comments
Couple of small changes, one reference added. To appear in Tokyo Journal of Mathematics