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Publications (21)

math.DS2025

Shadowing With Small Diameter Sets Of Bounded Cardinality

Jonathan Meddaugh, Elyssa Stephens

We examine dynamical systems with the property that pseudo-orbits can be traced by small diameter sets with bounded cardinality. In particular, we show that mixing sofic subshifts…

math.CO2022

On the $P_{3}$ -hull number and infecting times of generalized Petersen graphs

Daniel Herden, Jonathan Meddaugh, Mark Sepanski +8

The $P_{3}$ -hull number of a graph is the minimum cardinality of an infecting set of vertices that will eventually infect the entire graph under the rule that uninfected nodes become…

math.CO2024

On Criticality and Additivity of the Pseudoachromatic Number Under Join

Jonathan Meddaugh, Mark R. Sepanski, Yegnanarayanan Venkataraman

A vertex coloring of a graph is said to be pseudocomplete if, for any two distinct colors, there exists at least one edge with those two colors as its end vertices. The pseudoachro…

math.DS2021

Shadowing as a Structural Property of the Space of Dynamical Systems

Jonathan Meddaugh

We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems…

math.CO2024

Limits and Periodicity of Metamour $2$ -Distance Graphs

William Q. Erickson, Daniel Herden, Jonathan Meddaugh +3

Given a finite simple graph $G$ , let $M (G)$ denote its 2-distance graph, in which two vertices are adjacent if and only if they have distance 2 in $G$ . In this paper…

math.DS2008

Any counterexample to Makienko's conjecture is an indecomposable continuum

Clinton P. Curry, John C. Mayer, Jonathan Meddaugh +1

Makienko's conjecture, a proposed addition to Sullivan's dictionary, can be stated as follows: The Julia set of a rational function R has buried points if and only if no component…

math.CO2024

Robinson-Schensted shapes arising from cycle decompositions

Martha Du Preez, William Q. Erickson, Jonathan Feigert +5

In the symmetric group $S_{n}$ , each element $I ¨ $ has an associated cycle type $I^\pm$ , a partition of $n$ that identifies the conjugacy class of $I ¨ $ . The Robinson-Schensted (RS) corre…

math.DS2020

A characterization of $I ¨ $ -limit sets in subshifts of Baire space

Jonathan Meddaugh, Brian Raines

In this paper we consider the structure of $I ¨ $ -limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate t…

math.CO2025

Chromatic numbers with closed local modular constraints

Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski +9

Generalizing the notion of odd-sum colorings, a $Z$ -labeling of a graph $G$ is called a closed coloring with remainder $k mod n$ if the closed neighborhood label sum of ea…

math.DS2023

Specification and $I ¨ $ -chaos in non-compact systems

Cordell Hammon, Jonathan Meddaugh, Jasmin Mohn +1

In this paper, we demonstrate conditions under which a LindelÃ¶f dynamical system exhibits $I ¨ $ -chaos. In particular, if a system exhibits a generalized version of the specificatio…

math.CO2023

Young tableau reconstruction via minors

William Q. Erickson, Daniel Herden, Jonathan Meddaugh +4

The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau $T$ , a 1-minor of $T$ is a tableau obtained by first deleting…

math.DS2020

Shadowing, internal chain transitivity and $I^\pm$ -limit sets

Chris Good, Jonathan Meddaugh, Joel Mitchell

Let $f : X \to X$ be a continuous map on a compact metric space $X$ and let $I^\pm_{f}$ , $I ¨ _{f}$ and $I C T_{f}$ denote the set of $I^\pm$ -limit sets, $I ¨ $ -limit sets and nonempty closed i…

math.DS2019

Limit Sets and Internal Transitivity in Free Group Actions

Kyle Binder, Jonathan Meddaugh

It has been recently shown that, under appropriate hypotheses, the $I ¨ $ -limit sets of a dynamical system are characterized by internal chain transitivity. In this paper, we examine…

math.DS2017

Shifts of finite type as fundamental objects in the theory of shadowing

Chris Good, Jonathan Meddaugh

Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fu…

math.CO2025

Chromatic numbers with open and nonzero local modular constraints

Daniel Herden, Jonathan Meddaugh, Mark R. Sepanski +9

In this paper, we explore chromatic numbers subject to various local modular constraints. For fixed $n$ , we consider proper integer colorings of a graph $G$ for which the closed an…

math.DS2020

Expansivity and unique shadowing

Chris Good, Sergio MacÃas, Jonathan Meddaugh +2

Let $f : X \to X$ be a continuous function on a compact metric space. We show that shadowing is equivalent to backwards shadowing and two-sided shadowing when the map $f$ is ont…

math.CO2026

Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux

Daniel Herden, Markus Hunziker, Jonathan Meddaugh +9

Young tableaux are fundamental objects in algebraic combinatorics and representation theory, with operations such as promotion and jeu de taquin playing a central role in their str…

math.DS2021

Shadowing, recurrence, and rigidity in dynamical systems

Jonathan Meddaugh

In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if…

math.CO2022

Klein cordial trees and odd cyclic cordial friendship graphs

William Q. Erickson, Daniel Herden, Jonathan Meddaugh +7

For a graph $G$ and an abelian group $A$ , a labeling of the vertices of $G$ induces a labeling of the edges via the sum of adjacent vertex labels. Hovey introduced the notion of an…

math.DS2021

On genericity of shadowing in one dimension

Jonathan Meddaugh

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.

math.CO2022

Vertex-edge marking score of certain triangular lattices

Daniel Herden, Jonathan Meddaugh, Mark Sepanski +8

The vertex-edge marking game is played between two players on a graph, $G = (V, E)$ , with one player marking vertices and the other marking edges. The players want to minimize/maximiz…

Publications (21)

Shadowing With Small Diameter Sets Of Bounded Cardinality

On the P3​-hull number and infecting times of generalized Petersen graphs

On Criticality and Additivity of the Pseudoachromatic Number Under Join

Shadowing as a Structural Property of the Space of Dynamical Systems

Limits and Periodicity of Metamour 2-Distance Graphs

Any counterexample to Makienko's conjecture is an indecomposable continuum

Robinson-Schensted shapes arising from cycle decompositions

A characterization of I¨-limit sets in subshifts of Baire space

Chromatic numbers with closed local modular constraints

Specification and I¨-chaos in non-compact systems

Young tableau reconstruction via minors

Shadowing, internal chain transitivity and I^±-limit sets

Limit Sets and Internal Transitivity in Free Group Actions

Shifts of finite type as fundamental objects in the theory of shadowing

Chromatic numbers with open and nonzero local modular constraints

Expansivity and unique shadowing

Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux

Shadowing, recurrence, and rigidity in dynamical systems

Klein cordial trees and odd cyclic cordial friendship graphs

On genericity of shadowing in one dimension

Vertex-edge marking score of certain triangular lattices

On the $P_{3}$ -hull number and infecting times of generalized Petersen graphs

Limits and Periodicity of Metamour $2$ -Distance Graphs

A characterization of $I ¨ $ -limit sets in subshifts of Baire space

Specification and $I ¨ $ -chaos in non-compact systems

Shadowing, internal chain transitivity and $I^\pm$ -limit sets