Matrix-valued orthogonal polynomials related to hexagon tilings

In this paper, we study a class of matrix-valued orthogonal polynomials (MVOPs) that are related to 2-periodic lozenge tilings hexagon. The general model depends on many parameters. the cases constant and parameter values show MVOP can be expressed in terms scalar with non-Hermitian orthogonality closed contour complex plane. hexagon tiling has phase transition large size limit. This is reflected asymptotic behavior as degree tends infinity. connection allows us find limiting zeros determinant MVOP. tend curve Σ ˜ 0 plane self-intersection. individual entries different behavior, zero distribution upper right entry under geometric condition were unable prove, but which convincingly supported by numerical evidence.