We introduce the notion of a Whitney dual of a graded poset. Two posets are Whitney duals to each other if (the absolute value of) their Whitney numbers of the first and second kind are interchanged between the two posets. We define new types of edge labelings which we call Whitney labelings. We prove that every graded poset with a Whitney labeling has a Whitney dual. Moreover, we show how to explicitly construct a Whitney dual using a technique involving quotient posets.

As applications of our main theorem, we show that geometric lattices and the lattice of noncrossing partitions all have Whitney duals. Our technique gives a combinatorial description of the Whitney dual of the partition lattice in terms of a poset of increasing forests. More generally we give combinatorial descriptions of Whitney duals of geometric lattices in terms of NBC sets. We also provide a combinatorial description of a Whitney dual of the noncrossing partition lattice in terms of collections of decorated Dyck paths.

Finally, we show that a graded poset with a Whitney labeling admits a local action of the 0-Hecke algebra of type A on its set of maximal chains. The characteristic of the associated representation is Ehrenborg's flag quasisymmetric function of the poset. The existence of this action implies, using a result of McNamara, that when the maximal intervals of the constructed Whitney duals are bowtie-free, they are also snellable. In the case where these maximal intervals are lattices, they are supersolvable.

我们介绍了渐变摆球的惠特尼对偶的概念。如果两个体态的第一和第二类惠特尼数（的绝对值）在两个体态之间互换，则它们是惠特尼对偶。我们定义了新的边缘标签类型，我们将其称为Whitney标签。我们证明，每个带有惠特尼标签的分级摆球都具有惠特尼对偶。此外，我们展示了如何使用涉及商态的技术显式构造Whitney对偶。

作为主定理的应用，我们证明了几何格和非交叉分区的格都具有惠特尼对偶。我们的技术根据不断增加的森林的势态给出了分隔格的惠特尼对偶的组合描述。更一般地，我们根据NBC集给出几何格子的惠特尼对偶的组合描述。我们还根据装饰性Dyck路径的集合提供了非交叉分区格的Whitney对偶的组合描述。

最后，我们证明了一个带有Whitney标签的渐进式球型在其最大链集上承认A型0-Hecke代数的局部作用。关联表示的特征是摆姿势的埃伦堡（Ehrenborg）标志准对称函数。使用McNamara的结果，该动作的存在意味着，当所构造的Whitney对偶的最大间隔为无领结时，它们也是可吸引的。在这些最大间隔是晶格的情况下，它们是超可解的。