Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

TL;DR

This paper explores the connection between two different methods for analyzing periodic box-ball systems, clarifying how rigged configurations relate to 10-elimination techniques.

Contribution

It precisely describes the interrelations between the rigged configuration approach and the 10-elimination approach for periodic box-ball systems.

Findings

Established a detailed correspondence between the two approaches.

Enhanced understanding of the initial value problem in box-ball systems.

Provided a unified framework for future research.

Abstract

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba--Takagi--Takenouchi and another way is the 10-elimination approach due to Mada--Idzumi--Tokihiro. In this paper, we describe precisely interrelations between these two approaches.