Let \(\mathcal S\) be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of \(\mathcal S\) by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

令\（\ mathcal S \）为具有任意层数的单条件Schubert变体。最近，在第二作者的论文中获得了对适用于这种变体的分解定理的求和式的明确描述。从该结果开始，我们通过其层的Poincaré多项式对\（\ mathcal S \）的交调和项的Poincaré多项式进行了明确的描述，获得了与几个Grassmannian的Poincaré多项式相关的有趣的多项式恒等式，两者均由从本地和全球角度来看。我们还将对这些身份的特定案例进行象征性研究。