  We show that for a special alternating link diagram, the following three
polynomials are essentially the same: a) the part of the HOMFLY polynomial that
corresponds to the leading term in the Alexander polynomial; b) the $h$-vector
for a triangulation of the root polytope of the Seifert graph and c) the
enumerator of parking functions for the planar dual of the Seifert graph. These
observations yield formulas for the maximal $z$-degree part of the HOMFLY
polynomial of an arbitrary homogeneous link as well. Our result is part of a
program aimed at reading HOMFLY coefficients out of Heegaard Floer homology.
