Upper bounds on the growth rates of independent sets in two dimensions via corner transfer matrices

DOI10.1016/j.laa.2018.06.008zbMath1392.05087OpenAlexW2807944195WikidataQ129655092 ScholiaQ129655092MaRDI QIDQ1654390

Yao-ban Chan, Andrew Rechnitzer

Publication date: 8 August 2018

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2018.06.008

zbMATH Keywords

independent setshard squarescorner transfer matrix

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Eigenvalues, singular values, and eigenvectors (15A18) Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Asymptotic enumeration (05A16) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Uses Software

• MPFR
• Eigen

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Enumerating independent vertex sets in grid graphs
• Approximating the hard square entropy constant with probabilistic methods
• The channel capacity of read/write isolated memory
• Sequential cavity method for computing free energy and surface pressure
• Planar lattice gases with nearest-neighbor exclusion
• On the channel capacity of read/write isolated memory
• Unzerlegbare, nicht negative Matrizen
• Corner Transfer Matrix Renormalization Group Method
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• The statistics of dimers on a lattice
• Accurate Lower Bounds on 2-D Constraint Capacities From Corner Transfer Matrices
• Exact and Approximate Compression of Transfer Matrices for Graph Homomorphisms
• Series expansions from the corner transfer matrix renormalization group method: the hard-squares model
• The entropies of topological Markov shifts and a related class of algebraic integers
• MPFR
• Enumeration of structure-sensitive graphical subsets: Theory
• Enumeration of structure-sensitive graphical subsets: Calculations
• The Number of Independent Sets in a Grid Graph
• An Introduction to Symbolic Dynamics and Coding
• Series expansions from the corner transfer matrix renormalization group method: II. Asymmetry and high-density hard squares
• The $1$-Vertex Transfer Matrix and Accurate Estimation of Channel Capacity
• Improved Lower Bounds on Capacities of Symmetric 2D Constraints Using Rayleigh Quotients
• Dimer problem in statistical mechanics-an exact result
• The undecidability of the domino problem

This page was built for publication: Upper bounds on the growth rates of independent sets in two dimensions via corner transfer matrices