Hard Square Entropy Constant
N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Let 
be the number of binary 
Matrices with no adjacent 1s (in either columnsor rows). Define 
, then the hard square entropy constant is defined by
The quantity
arises in statistical physics (Baxter et al. 1980, Pearce and Seaton 1988), and is known as theentropy per site of hard squares. A related constant known as the Hard Hexagon Entropy Constant can also bedefined.
References
Baxter, R. J.; Enting, I. G.; and Tsang, S. K. ``Hard-Square Lattice Gas.'' J. Statist. Phys. 22, 465-489, 1980. Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/square/square.html Pearce, P. A. and Seaton, K. A. ``A Classical Theory of Hard Squares.'' J. Statist. Phys. 53, 1061-1072, 1988.
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