Ultradiscrete Painlevé VI with Parity Variables

We introduce a ultradiscretization with parity variables of the $q$-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of $q$-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those of ultradiscrete Painlevé VI equation.