Higher-order generalizations of the $A_6^{(1)}$- and $A_4^{(1)}$-surface type $q$-Painlevé equations

In this paper, we construct higher-order generalizations of the $A_6^{(1)}$- and $A_4^{(1)}$-surface type $q$-Painlevé equations from the system of partial difference equations with the consistency around a cube property by periodic reduction. Moreover, we also show their extended affine Weyl group symmetries and Lax pairs.