Box-ball system: soliton and tree decomposition of excursions

DAVIDE GABRIELLI; PABLO A. FERRARI

arXiv

Cornell University

Lugar: Ithaca; Año: 2019

We review combinatorial properties of solitons of the Box-Ball system introduced by Takahashi and Satsuma. Starting with several definitions of the system, we describe ways to identify solitons and review a proof of the conservation of the solitons under the dynamics. Ferrari, Nguyen, Rolla and Wang proposed a soliton decomposition of an excursion over the current minima of the walk representative of a ball configuration. Building on this approach, we propose a new soliton decomposition which is equivalent to the classical branch decomposition of the tree associated to the excursion. When the ball occupation numbers are independent Bernoulli variables of parameter λ