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arXiv · 2501.03037

The Lehmer complex of a Bruhat interval

Davide Bolognini·Paolo Sentinelli
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Abstract

We introduce Lehmer codes, with immersions in the Bruhat order, for several finite Coxeter groups, including all the classical Weyl groups. This allows to associate to each lower Bruhat interval of these groups a multicomplex whose f-polynomial is the Poincaré polynomial of the interval. Via a general construction, we prove that these polynomials are h-polynomials of vertex-decomposable simplicial complexes. Moreover we provide a classification, in terms of unimodal permutations, of Poincaré polynomials of smooth Schubert varieties in flag manifolds.

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Davide Bolognini, Paolo Sentinelli. 2026-08-19. The Lehmer complex of a Bruhat interval. https://arxiv.org/abs/2501.03037

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