Knot Floer homology is a filtered version of Heegaard Floer homology, due to Ozsváth and Szabó, and Rasmussen in references  and . The `hat' version HFK-hat(S^3, Y) is a bigraded vector space over Z/2Z.
The data for HFK-hat displayed in this database, along with the invariants epsilon, nu, tau, and the L-space knot property were computed using a program written by Zoltan Szabó, available at . The calculations were performed with Z/2Z coefficients.
Example to clarify notation: The Poincare polynomial for HFK-hat of the trefoil is
 Ozsváth, P., Szabó, Z., "Holomorphic disks and knot invariants", Adv. Math. 186 (2004), no. 1, 58--116
 Rasmussen, J. "Floer homology and knot complements", Ph.D. thesis, Harvard University, 2003, arXiv:math.GT/0306378.
 Szabó, Z., Knot Floer Homology Calculator.