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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 181, Number 2, Pages 349–357
DOI: https://doi.org/10.4213/tmf8643 (Mi tmf8643) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Enumeration of plane partitions with a restricted number of parts

A. Rovenchak

Department for Theoretical Physics, Ivan Franko National University of Lviv, Lviv, Ukraine
Full-text PDF (376 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf8643
Abstract: We use the quantum statistical approach to estimate the number of restricted plane partitions of an integer n with the number of parts not exceeding some finite N. We use the analogy between this number theory problem and the enumeration of microstates of the ideal two-dimensional Bose gas. The numbers of restricted plane partitions calculated with the conjectured expression agree well with the exact values for n from 10 to 20.
Keywords: Bose gas, plane partition, restricted partition.
Received: 19.01.2014
Revised: 22.04.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 181, Issue 2, Pages 1428–1434
DOI: https://doi.org/10.1007/s11232-014-0223-5
Bibliographic databases:
PACS: 05.30.Ch, 05.30.Jp
MSC: 05A17, 11P81, 11P82
Language: Russian
Citation: A. Rovenchak, “Enumeration of plane partitions with a restricted number of parts”, TMF, 181:2 (2014), 349–357; Theoret. and Math. Phys., 181:2 (2014), 1428–1434
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8643
  • https://www.mathnet.ru/eng/tmf/v181/i2/p349
    • This publication is cited in the following 1 articles:
    1. Ch.-Ch. Zhou, W.-Sh. Dai, “A statistical mechanical approach to restricted integer partition functions”, J. Stat. Mech.-Theory Exp., 2018, 053111  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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