Constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations

We investigate two topics of the constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations. For the constrained dKP hierarchy, the constraint on the Lax operator $(L^k)_{<0}=q\Delta^{-1}r$ is shown to be equivalent to a constraint on the tau function, which provides another description of the constrained dKP hierarchy. We also find that there are two different choices of the generating functions in gauge transformation operators of the constrained discrete KP hierarchy.