Title: Power series expansions for the planar monomer-dimer problem,
Abstract: We compute the free energy of the planar monomer-dimer model. Unlike the
classical planar dimer model, an exact solution is not known in this case. Even
the computation of the low-density power series expansion requires heavy and
nontrivial computations. Despite of the exponential computational complexity,
we compute almost three times more terms than were previously known. Such an
expansion provides both lower and upper bound for the free energy, and allows
to obtain more accurate numerical values than previously possible. We expect
that our methods can be applied to other similar problems.