Abstract
The generating functions of models of directed walks pulled by an external force f are determined using the kernel method. These paths are models of linear polymers subject to an external force. The generating function is related to the generating function of ballot paths, and has an unexpected and non-physical singularity for the model of Dyck paths pulled at its central vertex. In each model the force–extension curve is determined exactly, and has a sigmoid shape partially given by Ctanh (cf) if f is the applied force and where c and C are the model-dependent constants. This result is consistent with previous results for models of pulled directed paths, and also with data obtained from the numerical simulation of self-avoiding walk models of linear polymers.
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