Labeled Chip-Firing on Star Graphs
Annika Gonzalez-Zugasti, Ryan Lynch, Dylan Snustad
TL;DR
This paper investigates the labeled chip-firing game on star graphs, proving a sorting property and analyzing stable configurations linked to Young tableaux, enhancing understanding of chip-firing dynamics.
Contribution
It introduces a sorting property for labeled chip-firing on star graphs and connects stable configurations to Young tableaux, providing new theoretical insights.
Findings
Proves a sorting property for the game.
Analyzes stable configurations related to Young tableaux.
Provides a mathematical framework for chip-firing on star graphs.
Abstract
We study the stable configurations of the labeled chip-firing game on an infinitely subdivided -star graph starting with chips on the center vertex. We prove a sorting property of this game and analyze special stable configurations corresponding to standard Young tableaux.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Cellular Automata and Applications · Stochastic processes and statistical mechanics