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.
From: Paolo Sentinelli [view email]
[v1]
Mon, 6 Jan 2025 14:24:46 UTC (25 KB)
[v2]
Wed, 5 Feb 2025 13:48:07 UTC (25 KB)
[v3]
Mon, 21 Jul 2025 16:46:43 UTC (25 KB)
[v4]
Mon, 8 Sep 2025 16:14:21 UTC (26 KB)
[v5]
Wed, 19 Aug 2026 15:13:45 UTC (27 KB)
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