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We determine, by hierarchy, dependencies between higher order linear symmetries which occur when generating them using recursion operators. Thus, we deduce a formula which gives the number of independent generalized symmetries (basis) of several orders. We construct a basis for conservation laws (with respect to the group admitted by the system of differential equation) and hence generate infinite conservation laws in each equivalence class.

A BASIS OF HIERARCHY OF GENERALIZED SYMMETRIES AND THEIR CONSERVATION LAWS FOR THE (3+1)-DIMENSIONAL DIFFUSION EQUATIONA