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By using the asymptotic theory of Pemantle and Wilson, exact asymptoticexpansions of the free energy of the monomer-dimer model on rectangular $n\times \infty$ lattices in terms of dimer density are obtained for small valuesof $n$, at both high and low dimer density limits. In the high dimer densitylimit, the theoretical results confirm the dependence of the free energy on theparity of $n$, a result obtained previously by computational methods. In thelow dimer density limit, the free energy on a cylinder $n \times \infty$lattice strip has exactly the same first $n$ terms in the series expansion asthat of infinite $\infty \times \infty$ lattice.Comment: 9 pages, 6 table

Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices