Hurwitz Orbits with a Cellular Automaton
Abstract
Hurwitz orbits are the orbits of the braid group action on the powers of a rack. Hurwitz orbits for the action of the braid group on three strands are used in 21 and 22 for the classification of Nichols algebras. This classification is based on a combinatorial invariant called plague on the Hurwitz orbits. The method to calculate plagues on the Hurwitz orbits is formulated in 22 by using a cellular automaton on the Hurwitz orbits and their quotients. By using this cellular automaton-based method we estimate the minimal plagues on the Hurwitz orbits.
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