We use a new algorithm for calculating the exact number of self-avoiding walks on random binary lattices made of open and closed sites. We provide a simple method for estimating the average value of this number for Monte Carlo-generated lattices. We also present their statistical distribution, and explain the observed trends in this distribution. Finally, we mention several potential applications of these calculations and comment on the relation to the localization-function theory which is to appear in a future paper.
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Rexakis et al. (1983) studied this question.
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