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Palindromic Poincaré polynomials in $B_n$
We describe the set of palindromic Poincaré polynomials in $B_n$. As a key ingredient in this classification, we prove that $A_n$ embeds into $B_n$ as a lower interval in Bruhat order. Consequently, all Poincare polynomials $P_w(q)$ and all Kazhdan--Lusztig polynomials $P_{x,y}(q)$ of $A_n$ occur in
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