The Lehmer complex of a Bruhat interval
Combinatorics
2025-09-09 v4
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 Poincar\'e 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 Poincar\'e polynomials of smooth Schubert varieties in flag manifolds.
Cite
@article{arxiv.2501.03037,
title = {The Lehmer complex of a Bruhat interval},
author = {Davide Bolognini and Paolo Sentinelli},
journal= {arXiv preprint arXiv:2501.03037},
year = {2025}
}