A weak Lehmer code for type $F_4$
Combinatorics
2026-05-13 v2
Abstract
We provide an algorithm to construct a multicomplex for any lower Bruhat interval of , such that its rank--generating function equals that of the Bruhat interval. For Weyl groups, it is always possible to find such a multicomplex thanks to the work of Bj\"{o}rner and Ekedahl. The algorithm is based on only two functions, which weaken the notion of Lehmer code for finite Coxeter groups, motivated by the fact that a strong Lehmer code for type does not exist. We also realize the set of palindromic Poincar\'e polynomials of as an induced subposet of the Bruhat order that forms a lattice.
Keywords
Cite
@article{arxiv.2509.20981,
title = {A weak Lehmer code for type $F_4$},
author = {Paolo Sentinelli and Andrea Zatti},
journal= {arXiv preprint arXiv:2509.20981},
year = {2026}
}