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TMF, 2007, Volume 150, Number 2, Pages 193–203 (Mi tmf5973)  

This article is cited in 13 scientific papers (total in 13 papers)

Enumeration of plane partitions and the algebraic Bethe anzatz

N. M. Bogolyubov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

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.

Keywords: integrable models, Bethe anzatz, plane partitions

DOI: https://doi.org/10.4213/tmf5973

Full text: PDF file (399 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2007, 150:2, 165–174

Bibliographic databases:

Received: 01.05.2006

Citation: N. M. Bogolyubov, “Enumeration of plane partitions and the algebraic Bethe anzatz”, TMF, 150:2 (2007), 193–203; Theoret. and Math. Phys., 150:2 (2007), 165–174

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. M. Bogolyubov, “Four-vertex model”, J. Math. Sci. (N. Y.), 151:2 (2008), 2816–2828  mathnet  crossref  mathscinet
    2. N. M. Bogolyubov, “Four-vertex model and random tilings”, Theoret. and Math. Phys., 155:1 (2008), 523–535  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. J. Math. Sci. (N. Y.), 158:6 (2009), 771–786  mathnet  crossref  zmath
    4. Nikolay M. Bogolyubov, “Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model”, SIGMA, 5 (2009), 052, 11 pp.  mathnet  crossref  mathscinet  zmath
    5. N. M. Bogolyubov, “Five vertex model with fixed boundary conditions”, St. Petersburg Math. J., 21:3 (2010), 407–421  mathnet  crossref  mathscinet  zmath  isi
    6. Bogoliubov N., Timonen J., “Correlation functions for a strongly coupled boson system and plane partitions”, Philos Trans R Soc Lond Ser A Math Phys Eng Sci, 369:1939 (2011), 1319–1333  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. N. M. Bogolyubov, “Combinatorics of a strongly coupled boson system”, Theoret. and Math. Phys., 181:1 (2014), 1132–1144  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    8. A. Rovenchak, “Enumeration of plane partitions with a restricted number of parts”, Theoret. and Math. Phys., 181:2 (2014), 1428–1434  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    9. Pozsgay B., “Quantum Quenches and Generalized Gibbs Ensemble in a Bethe Ansatz Solvable Lattice Model of Interacting Bosons”, J. Stat. Mech.-Theory Exp., 2014, P10045  crossref  mathscinet  isi  scopus
    10. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Pozsgay B., Eisler V., “Real-time dynamics in a strongly interacting bosonic hopping model: global quenches and mapping to the XX chain”, J. Stat. Mech.-Theory Exp., 2016, 053107  crossref  mathscinet  isi  elib  scopus
    12. Bogoliubov N., Malyshev C., “The Phase Model and the Norm-Trace Generating Function of Plane Partitions”, J. Stat. Mech.-Theory Exp., 2018, 083101  crossref  isi  scopus
    13. Zhou Ch.-Ch., Dai W.-Sh., “A Statistical Mechanical Approach to Restricted Integer Partition Functions”, J. Stat. Mech.-Theory Exp., 2018, 053111  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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