Discrete zero curvature representations and infinitely many conservation laws for several 2+1 dimensional lattice hierarchies

In this article, several 2+1 dimensional lattice hierarchies proposed by Blaszak and Szum [J. Math. Phys. {\bf 42}, 225(2001)] are further investigated. We first describe their discrete zero curvature representations. Then, by means of solving the corresponding discrete spectral equation, we demonstrate the existence of infinitely many conservation laws for them and obtain the corresponding conserved densities and associated fluxes formulaically. Thus, their integrability is further confirmed.