Linearization of the box-ball system with box capacity L
Exactly Solvable and Integrable Systems
2025-08-19 v3 Mathematical Physics
math.MP
Abstract
We construct a bijection between the state of the box-ball system with box capacity L and a pair of two sequences. In time evolution, one of the sequences moves at speed 1, and the other follows the rules of the box-ball system with box capacity one, which can be linearized by the Kerov-Kirillov-Reshetikhin(KKR) bijection. Our method can be applied to a state including a negative value or a value greater than the box capacity.
Cite
@article{arxiv.2207.08066,
title = {Linearization of the box-ball system with box capacity L},
author = {Atsushi Maeno and Satoshi Tsujimoto},
journal= {arXiv preprint arXiv:2207.08066},
year = {2025}
}
Comments
This version contains corrections of typos and minor clarifications. 20pages, 12 figures