Motzkin numbers out of Random Domino Automaton
Mariusz Bia{\l}ecki
TL;DR
This paper derives Motzkin numbers from a specific case of the Random Domino Automaton, providing an exact solution and linking it to the automaton's asymptotic behavior, thus connecting combinatorics with earthquake modeling.
Contribution
It presents an exact solution for the stationary state of the automaton in the inverse-power case and establishes a novel connection to Motzkin numbers.
Findings
Explicit form of the automaton's asymptotic behavior
Exact solution for the stationary state in the inverse-power case
Link between Motzkin numbers and the automaton's dynamics
Abstract
Motzkin numbers are derived from a special case of Random Domino Automaton - recently proposed toy model of earthquakes. An exact solution of the set of equations describing stationary state of Random Domino Automaton in "inverse-power" case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.
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