Spanning Trees of the Generalised Union Jack Lattice
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Lingyun Chen
Abstract
The Union Jack lattice UJL(n, m) with toroidal boundary condition can be obtained from an n×m square lattice with toroidal boundary condition by inserting a new vertex vf to each face f and adding four edges (vf, ui(f)), where u1(f), u2(f), u3(f), and u4(f) are four vertices on the boundary of f. The Union Jack lattice has been studied extensively by statistical physicists. In this article, we consider the problem of enumeration of spanning trees of the so-called generalised Union Jack lattice UDn, which is obtained from the Aztec diamond
Acknowledgments
We are grateful to the anonymous referees for many friendly and helpful revising suggestions. The second author was supported in part by NSFC Grant (11171134, 11571139).
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Articles in the same Issue
- Frontmatter
- Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
- Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation
- Electrical Conduction in Transition-Metal Salts
- Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene
- Understanding the Formation Mechanism of Two-Dimensional Atomic Islands on Crystal Surfaces by the Condensing Potential Model
- The Thermodynamic Functions in Curved Space of Neutron Star
- Spanning Trees of the Generalised Union Jack Lattice
- Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
- Negative Energies in the Dirac Equation
- Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation
- Multifold Darboux Transformations of the Extended Bigraded Toda Hierarchy
- Unidirectional Excitation of Graphene Plasmon in Attenuated Total Reflection (ATR) Configuration
- Completed Optimised Structure of Threonine Molecule by Fuzzy Logic Modelling
Articles in the same Issue
- Frontmatter
- Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters
- Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation
- Electrical Conduction in Transition-Metal Salts
- Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene
- Understanding the Formation Mechanism of Two-Dimensional Atomic Islands on Crystal Surfaces by the Condensing Potential Model
- The Thermodynamic Functions in Curved Space of Neutron Star
- Spanning Trees of the Generalised Union Jack Lattice
- Prolongation Structure of a Generalised Inhomogeneous Gardner Equation in Plasmas and Fluids
- Negative Energies in the Dirac Equation
- Residual Symmetry and Explicit Soliton–Cnoidal Wave Interaction Solutions of the (2+1)-Dimensional KdV–mKdV Equation
- Multifold Darboux Transformations of the Extended Bigraded Toda Hierarchy
- Unidirectional Excitation of Graphene Plasmon in Attenuated Total Reflection (ATR) Configuration
- Completed Optimised Structure of Threonine Molecule by Fuzzy Logic Modelling
