%0 Journal Article %T Lax pairs of discrete Painlev¨¦ equations: $(A_2+A_1)^{(1)}$ case %A Nalini Joshi %A Nobutaka Nakazono %A Yang Shi %J Physics %D 2015 %I arXiv %X In this paper, we provide a comprehensive method for constructing Lax pairs of discrete Painlev\'e equations. In particular, we consider the $A_5^{(1)}$-surface $q$-Painlev\'e system which has the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$ and show two new Lax pairs. %U http://arxiv.org/abs/1503.04515v1