The Number of Independent Sets in a Grid Graph
The Number of Independent Sets in a Grid Graph
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 …