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Weighted enumerations of boxed plane partitions and the inhomogeneous five-vertex model. (English. Russian original) Zbl 1276.05007

J. Math. Sci., New York 192, No. 1, 70-80 (2013); translation from Zap. Nauchn. Semin. POMI 398, 125-144 (2012).
Summary: We consider the five-vertex model on a square lattice with fixed boundary conditions which corresponds to weighted (with weight \(q\) per elementary cube) enumerations of boxed plane partitions. We calculate the one-point correlation function of the model which describes the probability of a given state on an edge (polarization). This generalizes an analogous result obtained previously by the authors for unweighted (weighted with weight \(q=1\)) enumerations of plane partitions.

MSC:

05A17 Combinatorial aspects of partitions of integers
05A15 Exact enumeration problems, generating functions
05B45 Combinatorial aspects of tessellation and tiling problems
60C05 Combinatorial probability
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References:

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