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An ultradiscrete system corresponding to the $q$-Painlev\'e equation of type$A_6^{(1)}$, which is a $q$-difference analogue of the second Painlev\'eequation, is proposed. Exact solutions with two parameters are constructed forthe ultradiscrete system.

Exact Solutions with Two Parameters for an Ultradiscrete Painlev\'e Equation of Type $A_6^{(1)}$