In this talk I will explain the Bolognini–Sentinelli method to characterize Poincaré polynomials of smooth Schubert varieties in type A through unimodal permutations and a Lehmer code. Then, I will show that every Poincaré polynomial of Schubert varieties in type Aₙ occurs in type Bₙ. Combining this with a type Bₙ Lehmer code, I will characterize all palindromic polynomials of Schubert varieties in type Bₙ. If time permits, I will explain our joint work with Hu and Sentinelli on a further equivalence of smoothness of Schubert varieties in type A.