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Zap. Nauchn. Sem. POMI, 2008, Volume 360, Pages 162–179 (Mi znsl2164)  

This article is cited in 2 scientific papers (total in 2 papers)

The five-vertex model and boxed plane partitions

V. S. Kapitonova, A. G. Pronkob

a State Technological Institute of St. Petersburg
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Boxed plane partitions are considered in terms of the five-vertex model on a finite lattice with fixed boundary conditions. Assuming that all weights of the model have the same value, the one-point correlation function describing the probability of having a given state on an arbitrary horizontal edge of the lattice is calculated. This is equivalent to the enumeration of boxed plane partitions that correspond to rhombus tilings of a hexagon with one fixed rhombus of a particular type. The solution of the problem is given for the case of a box of generic size. Bibl. – 27 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 158:6, 858–867

Bibliographic databases:

UDC: 517.958
Received: 10.12.2008

Citation: V. S. Kapitonov, A. G. Pronko, “The five-vertex model and boxed plane partitions”, Representation theory, dynamics systems, combinatorial methods. Part XVI, Zap. Nauchn. Sem. POMI, 360, POMI, St. Petersburg, 2008, 162–179; J. Math. Sci. (N. Y.), 158:6 (2009), 858–867

Citation in format AMSBIB
\Bibitem{KapPro08}
\by V.~S.~Kapitonov, A.~G.~Pronko
\paper The five-vertex model and boxed plane partitions
\inbook Representation theory, dynamics systems, combinatorial methods. Part~XVI
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 360
\pages 162--179
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2164}
\zmath{https://zbmath.org/?q=an:05632972}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 158
\issue 6
\pages 858--867
\crossref{https://doi.org/10.1007/s10958-009-9423-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349175677}


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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. V. S. Kapitonov, A. G. Pronko, “Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model”, J. Math. Sci. (N. Y.), 192:1 (2013), 70–80  mathnet  crossref  mathscinet
    2. A. G. Pronko, “The five-vertex model and enumerations of plane partitions”, J. Math. Sci. (N. Y.), 213:5 (2016), 756–768  mathnet  crossref  mathscinet
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