Geodesic
Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 125-144 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The five-vertex model on a square lattice with fixed boundary conditions, which corresponds to the weighted (with the weight $q$ per elementary cube) enumerations of boxed plane partition is considered. The one-point correlation function of the model describing the probability of a given state on an edge (polarization) is calculated. This generalises the similar result obtained previously by the authors for the unweighed (weighted with the weight $q=1$) enumerations of plane partitions. 
@article{ZNSL_2012_398_a6,
     author = {V. S. Kapitonov and A. G. Pronko},
     title = {Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--144},
     year = {2012},
     volume = {398},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a6/}
}
TY  - JOUR
AU  - V. S. Kapitonov
AU  - A. G. Pronko
TI  - Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 125
EP  - 144
VL  - 398
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a6/
LA  - ru
ID  - ZNSL_2012_398_a6
ER  - 
%0 Journal Article
%A V. S. Kapitonov
%A A. G. Pronko
%T Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 125-144
%V 398
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a6/
%G ru
%F ZNSL_2012_398_a6
V. S. Kapitonov; A. G. Pronko. Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 125-144. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a6/

[1] G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing, 1976 | MR | Zbl

[2] D. M. Bressoud, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[3] H. Cohn, M. Larsen, J. Propp, “The shape of a typical boxed plane partition”, New York J. Math., 4 (1998), 137–165 | MR | Zbl

[4] Al. Borodin, V. Gorin, E. M. Rains, “$q$-Distributions on boxed plane partitions”, Selecta Math. (N.S.), 16 (2010), 731–789 | DOI | MR | Zbl

[5] N. M. Bogoliubov, “Boxed plane partitions as an exactly solvable boson model”, J. Phys. A, 38 (2005), 9415–9430 | DOI | MR | Zbl

[6] N. M. Bogolyubov, “Chetyrekhvershinnaya model i sluchainye ukladki”, Teor. mat. fiz., 155:1 (2008), 25–38 | DOI | MR | Zbl

[7] V. S. Kapitonov, A. G. Pronko, “Pyativershinnaya model i ploskie razbieniya v yaschike”, Zap. nauchn. semin. POMI, 360, 2008, 162–179 | MR | Zbl

[8] F. A. Berezin, Metod vtorichnogo kvantovaniya, 2-oe izd. (dop.), Nauka, M., 1986 | MR | Zbl

[9] R. Koekoek, P. A. Lesky, R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their $q$-Analogues, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2010 | DOI | MR | Zbl

[10] D. S. Moak, “The $q$-analogue of the Laguerre polynomials”, J. Math. Anal. Appl., 81 (1981), 20–47 | DOI | MR | Zbl

[11] R. Koekoek, “Generalizations of a $q$-analogue of Laguerre polynomials”, J. Approx. Theory, 69 (1992), 55–83 | DOI | MR | Zbl

[12] S. G. Moreno, E. M. García-Caballero, “$q$-Sobolev orthogonality of the $q$-Laguerre polynomials $\{L_n^{(-N)}(\cdot;q)\}_{n=0}^\infty$ for positive integers $N$”, J. Korean Math. Soc., 48 (2011), 913–926 | DOI | MR | Zbl

[13] G. Szegö, Orthogonal Polinomials, American Colloquium Publications, 23, 4th edn., American Mathematical Society, Providence, RI, 1975 | MR

[14] I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edn., Oxford University Press, Oxford, 1995 | MR | Zbl