The five-vertex model and boxed plane partitions

DOI10.1007/s10958-009-9423-1zbMath1231.05016OpenAlexW2089430908MaRDI QIDQ1036999

V. S. Kapitonov, Andrei G. Pronko

Publication date: 13 November 2009

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-009-9423-1

zbMATH Keywords

Young diagramfive-vertex model on a finite lattice with fired boundary conditions

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Combinatorial aspects of partitions of integers (05A17) Combinatorial probability (60C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Combinatorial aspects of tessellation and tiling problems (05B45)

Related Items (4)

Quantum Hamiltonians generated by the \(R\)-matrix of the five-vertex model ⋮ Six-vertex model as a Grassmann integral, one-point function, and the arctic ellipse ⋮ Weighted enumerations of boxed plane partitions and the inhomogeneous five-vertex model ⋮ Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain

Uses Software

• ROBBINS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Random skew plane partitions and the Pearcey process
• Quantum inverse scattering method for the \(q\)-boson model and symmetric functions
• Four-vertex model and random tilings
• Enumeration of quarter-turn-symmetric alternating-sign matrices of odd order
• Binomial determinants, paths, and hook length formulae
• The shape of a typical boxed plane partition
• The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. I
• Proof of the refined alternating sign matrix conjecture
• Step fluctuations for a faceted crystal
• The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. II
• Non-intersecting paths, random tilings and random matrices
• Four symmetry classes of plane partitions under one roof
• Four-vertex model
• Limit shapes and the complex Burgers equation
• Dimers and amoebae
• The Limit Shape of Large Alternating Sign Matrices
• Boxed plane partitions as an exactly solvable boson model
• A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• On the Vector Representations of Induced Matroids

This page was built for publication: The five-vertex model and boxed plane partitions