Combinatorial nature of ground state vector of O(1) loop model

Abstract

Hanging about a hypothetical connections between the ground state vector for some special spin systems and the alternating-sign matrices, we have found a numerical evidence for the fact that the numbers of the states of the fully packed loop model with fixed link-patterns coincide with the components of the ground state vector of the dense O$(1)$ loop model considered by Batchelor, de Gier and Nienhuis. Our conjecture generalizes in a sense the conjecture of Bosley and Fidkowski, refined by Cohn and Propp, and proved by Wieland.

5 pages, LaTeX2e, DFPL is changed to FPL in accordance with a suggestion of J. Propp

References in corpus (2)

• Spin chains and combinatorics: twisted boundary conditions
• A Large Dihedral Symmetry of the Set of Alternating Sign Matrices

Cited by in corpus (44)

• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• Temperley-Lieb Stochastic Processes
• Arctic curves of the six-vertex model on generic domains: the Tangent Method
• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• The XXZ spin chain at $\Delta =-1/2$: Bethe roots, symmetric functions and determinants
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Inhomogeneous loop models with open boundaries
• Totally Symmetric Self-Complementary Plane Partitions and Quantum Knizhnik-Zamolodchikov equation: a conjecture
• Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
• Combinatorial point for higher spin loop models
• Ground-state properties of a supersymmetric fermion chain
• Multiply-refined enumeration of alternating sign matrices
• Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models
• Koornwinder polynomials and the XXZ spin chain
• Keys and alternating sign matrices
• From Orbital Varieties to Alternating Sign Matrices
• The Rotor Model and Combinatorics
• On FPL configurations with four sets of nested arches
• Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identities
• Proof of Razumov-Stroganov conjecture for some infinite families of link patterns
• The Wave Functions for the Free-Fermion Part of the Spectrum of the $S{U}_q(N)$ Quantum Spin Models
• A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule
• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the sum rule
• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the ground state
• A conjectured formula for Fully Packed Loop configurations in a triangle
• Currents in the dilute $O(n=1)$ model
• Fully packed loop models on finite geometries
• The many faces of alternating-sign matrices
• A Positive integral property on the ground state of the two-boundary Temperley--Lieb Hamiltonian
• Grassmann-Grassmann conormal varieties, integrability, and plane partitions
• Density profiles in the raise and peel model with and without a wall. Physics and combinatorics
• Loop Models and $K$-Theory
• The Manhattan and Lorentz Mirror Models -- A result on the Cylinder with low density of mirrors
• The scalar product of XXZ spin chain revisited. Application to the ground state at $\Delta =-1/2$
• Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation
• Truncated determinants and the refined enumeration of Alternating Sign Matrices and Descending Plane Partitions
• On some polynomials enumerating Fully Packed Loop configurations
• A bijectional attack on the Razumov-Stroganov conjecture
• On some polynomials enumerating Fully Packed Loops configurations, evaluation at negative values
• Quantum affine Knizhnik-Zamolodchikov equations and quantum spherical functions, I
• A unifying poset perspective on alternating sign matrices, plane partitions, Catalan objects, tournaments, and tableaux