Random permutations and unique fully supported ergodicity for the Euler adic transformation

TL;DR

This paper proves the uniqueness of the fully supported ergodic invariant measure for the Euler adic transformation, providing insights into the distribution of random permutations and their ergodic properties.

Contribution

It establishes the uniqueness of the ergodic measure for the Euler adic transformation, linking it to the equidistribution of random permutations.

Findings

Unique fully supported ergodic invariant measure identified

Supports assumptions about random permutation equidistribution

Advances understanding of Euler adic transformation dynamics

Abstract

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.