215 citations · 1k across the 30 of their papers we have counts for
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A possible combinatorial point for XYZ-spin chain
A. V. Razumov, Yu. G. Stroganov
We formulate and discuss a number of conjectures on the ground state vectors of the XYZ-spin chains of odd length with periodic boundary conditions and a special choice of the Hami…
Three-coloring statistical model with domain wall boundary conditions. II. Trigonometric limit
A. V. Razumov, Yu. G. Stroganov
A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed…
Three-coloring statistical model with domain wall boundary conditions. I. Functional equations
A. V. Razumov, Yu. G. Stroganov
In 1970 Baxter considered the statistical three-coloring lattice model for the case of toroidal boundary conditions. He used the Bethe ansatz and found the partition function of th…
Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
A. V. Razumov, Yu. G. Stroganov, P. Zinn-Justin
Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered. It is proved that wh…
Bethe roots and refined enumeration of alternating-sign matrices
A. V. Razumov, Yu. G. Stroganov
The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to -1/2 and an odd number of sites is considered. Some linear…
Enumeration of quarter-turn symmetric alternating-sign matrices of odd order
A. V. Razumov, Yu. G. Stroganov
It was shown by Kuperberg that the partition function of the square-ice model related to the quarter-turn symmetric alternating-sign matrices of even order is the product of two si…
Enumerations of half-turn symmetric alternating-sign matrices of odd order
A. V. Razumov, Yu. G. Stroganov
It was shown by Kuperberg that the partition function of the square-ice model related to half-turn symmetric alternating-sign matrices of even order is the product of two similar f…
Izergin-Korepin determinant reloaded
Yu. G. Stroganov
We consider the Izergin-Korepin determinant [1] together with another determinant which was invented by Kuperberg [2]. He used these determinants to prove a formula for the total n…
On refined enumerations of some symmetry classes of ASMs
A. V. Razumov, Yu. G. Stroganov
Using determinant representations for partition functions of the corresponding square ice models and the method proposed recently by one of the authors, we investigate refined enum…
3-enumerated alternating sign matrices
Yu. G. Stroganov
Let be the total weight of the alternating sign matrices of order whose sole `1' of the first row is at the column and the weight of an individual matrix is…
A new way to deal with Izergin-Korepin determinant at root of unity
Yu. G. Stroganov
I consider the partition function of the inhomogeneous 6-vertex model defined on the by square lattice. This function depends on 2n spectral parameters and atta…