Ternary reversible number-conserving cellular automata are trivial

We introduce a novel method to study the reversibility of d-dimensional number-conserving multi-state cellular automata with the von Neumann neighborhood. We apply this method to ternary such cellular automata, for which, up to now, nothing was known about their reversibility. It turns out that they are all trivial: the only reversible such cellular automata are shifts that are intrinsically 1-dimensional.