2022/02/18 by Kobayashi, Katsuki, Tsujimoto, Satoshi
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2202.09094
The ε-BBS is the family of solitonic cellular automata obtained via the ultradiscretization of the elementary Toda orbits, which is a parametrized family of integrable systems unifying the Toda equation and the relativistic Toda equation. In this paper, we derive the ε-BBS with many kinds of balls and give its conserved quantities by the Schensted insertion algorithm which is introduced in combinatorics. To prove this, we extend birational transformations of the continuous elementary Toda orbits to the discrete hungry elementary Toda orbits.