We present a derivation of a formula that gives dynamics of an integrable cellular automation associated with crystal bases. This automaton is related to type affine Lie algebra and contains usual box-ball systems as a special case. The dynamics is described by means of such objects as carriers, particles, and antiparticles. We derive it from an analysis of a recently obtained formula of the combinatorial (an intertwiner between tensor products of crystals) that was found in a study of geometric crystals.
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