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The dimer problem arose in a thermodynamic study of diatomic molecules, andwas abstracted into one of the most basic and natural problems in bothstatistical mechanics and combinatoric mathematics. Given a rectangular latticeof volume V in d dimensions, the dimer problem loosely speaking is to count thenumber of different ways dimers (dominoes) may be laid down in the lattice(without overlapping) to completely cover it. Each dimer covers two neighboringvertices. It is known that the number of such coverings is roughly exp(lambda_dV) for some constant lambda_d as V goes to infinity. Herein we present amathematical argument for an asymptotic expansion for lambda_d in inversepowers of d, and the results of computer computations for the first few termsin the series. As a glaring challenge, we conjecture no one will compute thenext term in the series, due to the requisite computer time and storagedemands.

Computation of Terms in the Asymptotic Expansion of Dimer lambda_d for High Dimension