Some remarks on A1(1) soliton cellular automata
Abstract
In this short note, we describe the A1(1) soliton cellular automata as an evolution of a poset. This allows us to explain the conservation laws for the A1(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.
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