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We prove a recent conjecture on the duality relation for correlationfunctions of the Potts model for boundary spins of a planar lattice.Specifically, we deduce the explicit expression for the duality of the n-sitecorrelation functions, and establish sum rule identities in the form of theM\"obius inversion of a partially ordered set. The strategy of the proof is byfirst formulating the problem for the more general chiral Potts model. Theextension of our consideration to the many-component Potts models is alsogiven.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

On the duality relation for correlation functions of the Potts model