On the New Dimer lambdad x-Expansion, Triangular and Hexagonal Lattices too
Abstract
In recent work the author presented a formal expansion for lambdad associated to the dimer problem on a d-dimensional rectangular lattice. Expressed in terms of d it yielded a presumed asymptotic expansion for lambdad in inverse powers of d. We also considered an expansion in powers of x, a formal variable ultimately set equal to 1. We believe this series has better asymptotic properties than the expansion in inverse powers of d. We discuss this, and apply the same method to the two-dimensional triangular and hexagonal lattices. Viewed as a test of the x-expansion the results on those two lattices are satisfactory, if not thoroughly convincing.
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