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The diagrammatic representation of the kink number expansion for cyclized polymers. The dashed curve represents the KWLC theory which is the sum of the m kink contributions. In the interval between the kinks, the polymer is described by WLC, represented by the solid curves. For each m kink contribution, we sum over the kink position. In order to meet the tangent alignment conditions for cyclized polymers, we close the chain at a kink for kink number one or greater.
