Lattice gas generalization of the hard hexagon model. III.q-Trinomial coefficients
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In the first two papers in this series we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites, and we described the local densities in terms of elliptic theta functions. Here we present the mathematical theory behind our derivation of the local densities. Our work centers onq-analogs of trinomial coefficients.
Key wordsStatistical mechanics lattice statistics number theory hard hexagon model Rogers-Ramanujan identities trinomial coefficients q-series
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