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The Pfaffian structure of the boundary monomer correlation functions in thedimer-covering planar graph models is rederived through a combinatorial /topological argument. These functions are then extended into a larger family oforder-disorder correlation functions which are shown to exhibit Pfaffianstructure throughout the bulk. Key tools involve combinatorial switchingsymmetries which are identified through the loop-gas representation of thedouble dimer model, and topological implications of planarity.

Pfaffian Correlation Functions of Planar Dimer Covers