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 Poincar{e} polynomials of the intersection cohomology of $mathcal S$ by means of the Poincar{e} polynomials of its strata, obtaining interesting polynomial identities relating Poincar{e} 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.
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