A spanning tree model for the Heegaard Floer homology of a branched double-cover

Given a diagram of a link K in S3, we write down a Heegaard diagram for the branched-double cover Σ(K). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of the link diagram. Using this model, we make some computations of the homology HF ^ ( Σ ( K ) ) as a graded group. We also conjecture the existence of a δ-grading on HF ^ ( Σ ( K ) ) analogous to the δ-grading on knot Floer and Khovanov homology.