  The dimer problem arose in a thermodynamic study of diatomic molecules, and
was abstracted into one of the most basic and natural problems in both
statistical mechanics and combinatoric mathematics. Given a rectangular lattice
of volume V in d dimensions, the dimer problem loosely speaking is to count the
number of different ways dimers (dominoes) may be layed down on the lattice to
completely cover it. It is known that the number of such coverings is roughly
exp(lambda_d V) for some number lambda_d. The first terms in the expansion of
lambda_d have been known for about thirty years lambda_d ~ (1/2)ln(2d)-1/2
Herein we present a mathematical argument for an asymptotic expansion lambda_d
~ (1/2)ln(2d) -1/2 +(1/8)/d + (5/96)/d^2 +... with the first few terms given
explicitly.
