Linearization of the box-ball system with box capacity L
arXiv:2207.08066 · doi:10.7566/JPSJ.92.024003
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.
This version contains corrections of typos and minor clarifications. 20pages, 12 figures