  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.
