Casorati and Discrete Gram Type Determinant Representations of Solutions to the Discrete KP Hierarchy

Solutions to the discrete KP hierarchy are expressed by two types of determinants. The first expression is the Casorati determinant and the second one is the discrete Gram type determinant. In both cases, the difference formula for the determinants are given in a simple form and the bilinear equations of the hierarchy are reduced to the Laplace expansion for determinants.