Three-dimensional integer partitions provide a convenient representation ofcodimension-one three-dimensional random rhombus tilings. Calculating theentropy for such a model is a notoriously difficult problem. We applytransition matrix Monte Carlo simulations to evaluate their entropy with highprecision. We consider both free- and fixed-boundary tilings. Our resultssuggest that the ratio of free- and fixed-boundary entropies is$\sigma_{free}/\sigma_{fixed}=3/2$, and can be interpreted as the ratio of thevolumes of two simple, nested, polyhedra. This finding supports a conjecture byLinde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' inthree-dimensional random tilings.
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