Related papers: Six-Vertex, Loop and Tiling models: Integrability …
We present a class of one-to-one matching models with perfectly transferable utility. We discuss identification and inference in these separable models, and we show how their comparative statics are readily analyzed.
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
A summary of the construction procedure of generalized versions of Baxter's Q-operator is given. Illustrated by several figures and diagrams the use of representation theory is explained step-by-step avoiding technical details. The relation…
We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
This research will be helpful for people to display the 2-dimensiona projective models of 4-variable actual problems in many fields, in order to investigate deeply those actual problems. By using the theory of N-dimensional finite rotation…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We discuss irreducible highest weight representations of the sl(2) loop algebra and reducible indecomposable ones in association with the sl(2) loop algebra symmetry of the six-vertex model at roots of unity. We formulate an elementary…
We study the problem of tiling and packing in vector spaces over finite fields, its connections with zeroes of classical exponential sums, and with the Jacobian conjecture
Fully packed loop models describe the statistics of closely packed nested polygons on the square lattice. Many exact results can be obtained for these models, even for finite geometries, using their close relationship to alternating-sign…
We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinumerous to the quarter-turn symmetric domino tilings of an…
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…