Exact solutions for restricted walks with applications to polymers

Abstract

The combinatorial theory of runs is used to algebraically enumerate new classes of restricted random walks and restricted self-avoiding walks. The restrictions favour the local formation of either cis or trans configurations. Exact results are derived and presented for the connective constant and corresponding exponent value for walks on d-dimensional hypercubic lattices. Preliminary numerical results for the mean square end-to-end distance exponent are also given. Show more