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December 2010 The Euler Adic Dynamical System and Path Counts in the Euler Graph
Karl PETERSEN, Alexander VARCHENKO
Tokyo J. Math. 33(2): 327-340 (December 2010). DOI: 10.3836/tjm/1296483473

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.

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Karl PETERSEN. Alexander VARCHENKO. "The Euler Adic Dynamical System and Path Counts in the Euler Graph." Tokyo J. Math. 33 (2) 327 - 340, December 2010. https://doi.org/10.3836/tjm/1296483473

Information

Published: December 2010
First available in Project Euclid: 31 January 2011

zbMATH: 1213.37008
MathSciNet: MR2779260
Digital Object Identifier: 10.3836/tjm/1296483473

Subjects:
Primary: 05A10, 05A15, 37A05, 37A25
Secondary: 37A50, 37A55

Rights: Copyright © 2010 Publication Committee for the Tokyo Journal of Mathematics

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Vol.33 • No. 2 • December 2010
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