Approximately counting up to four (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Capacity Bounds for the 3-Dimensional (0, 1) Runlength Limited Channel
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
An Entropy Approach to the Hard-Core Model on Bipartite Graphs
Combinatorics, Probability and Computing
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Discrete Applied Mathematics
Graphs, partitions and Fibonacci numbers
Discrete Applied Mathematics
Enumeration problems for classes of self-similar graphs
Journal of Combinatorial Theory Series A
Coding of two-dimensional constraints of finite type by substitutions
Journal of Automata, Languages and Combinatorics
Sequential cavity method for computing limits of the log-partition function for lattice models
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Capacity bounds for two-dimensional asymmetric M-ary (0, k) and (d,∞) runlength-limited channels
IEEE Transactions on Communications
On row-by-row coding for 2-D constraints
IEEE Transactions on Information Theory
Improved lower bounds on capacities of symmetric 2-dimensional constraints using Rayleigh quotients
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Improved lower bounds on capacities of symmetric 2D constraints using Rayleigh quotients
IEEE Transactions on Information Theory
Two-dimensional constrained coding based on tiling
IEEE Transactions on Information Theory
Bounds on the rate of 2-D bit-stuffing encoders
IEEE Transactions on Information Theory
The 1-vertex transfer matrix and accurate estimation of channel capacity
IEEE Transactions on Information Theory
A novel method for counting models on grid Boolean formulas
MCPR'10 Proceedings of the 2nd Mexican conference on Pattern recognition: Advances in pattern recognition
New bounds on the capacity of multi-dimensional RLL-Constrained systems
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Variable ordering for the application of BDDs to the maximum independent set problem
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
| Hi-index | 0.30 |
If f(m,n) is the (vertex) independence number of the $m\times n$ grid graph, then we show that the double limit $\eta\eqdef\lim_{m,n\to\infty}f(m,n)^{1\over {mn}}$ exists, thereby refining earlier results of Weber [Rostock. Math. Kolloq., 34 (1988), pp. 28--36] and Engel [Fibonacci Quart.,, 28 (1990), pp. 72--78]. We establish upper and lower bounds for $\eta$ and {\it prove} that $1.503047782... \le \eta \le 1.5035148\ldots $. Numerical computations suggest that the true value of $\eta$ (the "hard square constant") is around 1.5030480824753323... .