The number of independent sets in a grid graph

被引：126
|
作者：
Calkin, NJ [1 ]
Wilf, HS
机构：
[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA
[2] Univ Penn, Dept Math, Philadelphia, PA 19104 USA
来源：
SIAM JOURNAL ON DISCRETE MATHEMATICS | 1998年 / 11卷 / 01期
关键词：
independent sets; grid graphs;
D O I：
10.1137/S089548019528993X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
If f(m; n) is the (vertex) independence number of the m x n grid graph, then we show that the double limit eta [GRAPHICS] lim(m,n-->infinity);n ! f(m; n) 1/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 prove that 1.503047782... is less-than-or-equal-to eta less-than-or-equal to 1.5035148.... Numerical computations suggest that the true value of eta (the "hard square constant") is around 1.5030480824753323....
引用
收藏
页码：54 / 60
页数：7
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