2019•Journal of Mathematical PhysicsRequires access

Catalan numbers out of a stochastic cellular automaton

Mariusz Białecki

Abstract

Having constructed a stochastic cellular automaton, which is a simple model of earthquakes and has a stationary state described by Motzkin numbers’ recurrence, we define a stochastic cellular automaton, whose stationary state is characterized by Catalan numbers’ recurrence. Thus we provide a new interpretation of Catalan numbers in terms of stochastic discrete dynamical systems.

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Key concepts: Cellular automaton, Stochastic cellular automaton, Catalan number, Block cellular automaton, Catalan, Mathematics, Continuous automaton, Deterministic automaton