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Zap. Nauchn. Sem. POMI, 2015, Volume 433, Pages 204–223 (Mi znsl6134)  

This article is cited in 1 scientific paper (total in 1 paper)

The five-vertex model and enumerations of plane partitions

A. G. Pronko

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We consider the five-vertex model on an $N\times2N$ lattice with fixed boundary conditions of a special type. We discuss a determinantal formula for the partition function in application to description of various enumrations of $N\times N\times (M-N)$ boxed plane partions. It is shown, that at the free-fermion point of the model, this formula reproduces MacMahon formula for the number of boxed plane partitions, while for generic weights (out of the free-fermion point) it describes enumerations with the weight depending on the cumulative number of jumps along vertical (or horisontal) rows. Various representations for the partition function, which describes such enumerations, are obtained.

Key words and phrases: vertex models, fixed boundary conditions, scalar products, boxed plane partitions, determinant representations, Hankel matrices, multiple integrals.

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English version:
Journal of Mathematical Sciences (New York), 2016, 213:5, 756–768

Bibliographic databases:

UDC: 517.9
Received: 16.04.2015

Citation: A. G. Pronko, “The five-vertex model and enumerations of plane partitions”, Questions of quantum field theory and statistical physics. Part 23, Zap. Nauchn. Sem. POMI, 433, POMI, St. Petersburg, 2015, 204–223; J. Math. Sci. (N. Y.), 213:5 (2016), 756–768

Citation in format AMSBIB
\Bibitem{Pro15}
\by A.~G.~Pronko
\paper The five-vertex model and enumerations of plane partitions
\inbook Questions of quantum field theory and statistical physics. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 433
\pages 204--223
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493687}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 213
\issue 5
\pages 756--768
\crossref{https://doi.org/10.1007/s10958-016-2737-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957609016}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. P. Pron'ko, A. G. Pronko, “Off-shell Bethe states and the six-vertex model”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 228–243  mathnet
  • Записки научных семинаров ПОМИ
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