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Some remarks on A_1^{(1)} soliton cellular automata

Susumu Ariki
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Abstract

In this short note, 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.

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Susumu Ariki. 2000-08-12. Some remarks on A_1^{(1)} soliton cellular automata. https://arxiv.org/abs/math/0008091

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