Title: An Asymptotic Expansion for the Dimer lambda_d
The dimer problem is to count the number of ways a d-dimensional
"chessboard" can be completely covered by non-overlapping dimers
(dominoes), each dimer covering two nearest neighbor boxes. The
number is ~exp(Lambda_d*V) as the volume V goes to infinity. It has
been long known lambda_d ~ (1/2)ln(d) +(1/2)(ln(2)-1) We derive an
asymptotic expansion whose first few terms are lambda_d ~ (1/2)ln(d)
+(1/2)(ln(2)-1) +(1/8)(1/d) + (5/96)(1/d^2) + (5/64)(1/d^3) The last term
here was calculated by computer, and we conjecture the next term will
never be explicitly computed ( just by reason of required computer time ).
The expansion is not yet rigorously established.