摘要: Lundstr\"om and Saud Maia Leite conjectured that the $f$-vector of the order polytope of the crown poset $\Ccal_{2n}$ is log-concave. We prove that it is strictly log-concave for $n\geq 1$ and bottom-heavy for $n\ge3$. After a reduction of the face-number formula, the resulting polynomial admits Lucas and Chebyshev representations. As a consequence, we also settle the corresponding conjecture for order polytopes of face lattices of polygons.
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