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We introduce an invariant of alternating knots and links (called here WRP),namely a pair of integer polynomials associated with their two checkerboardplanar graphs from their minimal diagram. We prove that the invariant iswell-defined and give its values obtained from calculations for some knots inthe tables. This invariant is strong enough to distinguish all knots in thetables with up to 10 crossings (including their mirror images).

A polynomial pair invariant of alternating knots and links