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Enumeration of Number-Conserving Cellular Automata Rules with Two Inputs
Henryk Fuks and Kate Sullivan

We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with q states and the set of balanced sequences with q terms. This allows to enumerate number-conserving CA. We also show that number-conserving rules are becoming increasingly rare as the number of states increases.

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