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.

中文翻译：

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根多面体、停车函数和 HOMFLY 多项式

我们证明，对于一个特殊的交替链接图，以下三个多项式本质上是相同的： a) HOMFLY 多项式中对应于亚历山大多项式中首项的部分；b) 用于 Seifert 图的根多面体的三角剖分的 $h$-vector 和 c) Seifert 图的平面对偶的停车函数的枚举器。这些观察结果也为任意齐次链接的 HOMFLY 多项式的最大 $z$-degree 部分生成公式。我们的结果是旨在从 Heegaard Floer 同源性中读取 HOMFLY 系数的程序的一部分。