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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 150, Number 2, Pages 193–203
DOI: https://doi.org/10.4213/tmf5973 (Mi tmf5973) 		 
This article is cited in 15 scientific papers (total in 15 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
Full-text PDF (399 kB) Citations (15)
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DOI: https://doi.org/10.4213/tmf5973
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.
Received: 01.05.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 150, Issue 2, Pages 165–174
DOI: https://doi.org/10.1007/s11232-007-0012-5
Bibliographic databases:
Language: Russian
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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  • https://www.mathnet.ru/eng/tmf5973
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  • https://www.mathnet.ru/eng/tmf/v150/i2/p193
    • This publication is cited in the following 15 articles:
    1. Pozsgay B. Gombor T. Hutsalyuk A. Jiang Yu. Pristyak L. Vernier E., “Integrable Spin Chain With Hilbert Space Fragmentation and Solvable Real-Time Dynamics”, Phys. Rev. E, 104:4 (2021), 044106  crossref  mathscinet  isi
    2. Hutsalyuk A., Pozsgay B., “Integrability Breaking in the One-Dimensional Bose Gas: Atomic Losses and Energy Loss”, Phys. Rev. E, 103:4 (2021), 042121  crossref  mathscinet  isi
    3. Bogoliubov N., Malyshev C., “The Phase Model and the Norm-Trace Generating Function of Plane Partitions”, J. Stat. Mech.-Theory Exp., 2018, 083101  crossref  mathscinet  isi  scopus
    4. 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
    5. 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
    6. 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
    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. 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
    11. 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
    12. N. M. Bogolyubov, “Five vertex model with fixed boundary conditions”, St. Petersburg Math. J., 21:3 (2010), 407–421  mathnet  crossref  mathscinet  zmath  isi
    13. 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
    14. J. Math. Sci. (N. Y.), 158:6 (2009), 771–786  mathnet  crossref  zmath
    15. N. M. Bogolyubov, “Four-vertex model”, J. Math. Sci. (N. Y.), 151:2 (2008), 2816–2828  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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