## Some Remarks on $A_1^{(1)}$ Soliton Cellular Automata

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 1, Page 143--156.

Ariki, Susumu
Some Remarks on $A_1^{(1)}$ Soliton Cellular Automata
We describe the $A_1^{(1)}$ soliton cellular automata as an evolution of a poset. This allows us to explain the conservation laws for the $A_1^{(1)}$ soliton cellular automata, one given by Torii, Takahashi and Satsuma, and the other given by Fukuda, Okado and Yamada, in terms of the stack permutations of states in a very natural manner. As a biproduct, we can prove a conjectured formula relating these laws.