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Enumeration of plane partitions and the algebraic Bethe anzatz

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Abstract

We establish a relation between an exactly solvable boson model and plane partitions, i.e., three-dimensional Young diagrams enclosed in a box of finite size, which allows representing the partition generating functions as correlation functions of an integrable model and deriving the MacMahon formulas for enumerating partitions using the quantum inverse scattering method.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

    N. M. Bogoliubov

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  1. N. M. Bogoliubov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 193–203, February, 2007.

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Bogoliubov, N.M. Enumeration of plane partitions and the algebraic Bethe anzatz. Theor Math Phys 150, 165–174 (2007). https://doi.org/10.1007/s11232-007-0012-5

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