Finite Factors of Bernoulli Schemes and Distinguishing Labelings of Directed Graphs

Author:

Lazowski Andrew,Shea Stephen M.

Abstract

A labeling of a graph is a function from the vertices of the graph to some finite set.  In 1996, Albertson and Collins defined distinguishing labelings of undirected graphs.  Their definition easily extends to directed graphs.  Let $G$ be a directed graph associated to the $k$-block presentation of a Bernoulli scheme $X$.  We determine the automorphism group of $G$, and thus the distinguishing labelings of $G$.  A labeling of $G$ defines a finite factor of $X$.  We define demarcating labelings and prove that demarcating labelings define finitarily Markovian finite factors of $X$.  We use the Bell numbers to find a lower bound for the number of finitarily Markovian finite factors of a Bernoulli scheme.  We show that demarcating labelings of $G$ are distinguishing.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the failure of Ornstein theory in the finitary category;Transactions of the American Mathematical Society;2024-04-09

2. Distinguishing numbers and distinguishing indices of oriented graphs;Discrete Applied Mathematics;2020-10

3. Optimal Domination Polynomials;Graphs and Combinatorics;2020-06-12

4. On the distinguishing number of cyclic tournaments: Towards the Albertson–Collins Conjecture;Discrete Applied Mathematics;2019-08

5. Harmonious Coloring on Corona Product of Complete Graphs;National Academy Science Letters;2014-09-16

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