A weak Lehmer code for type F₄

2025/09/25 by Sentinelli, Paolo, Zatti, Andrea · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.20981

Abstract

We show that, despite the Poincaré polynomial of F₄ is a product of q-analogues, the Bruhat order of F₄ does not admit a product of chains as subposet. This answers negatively, in this type, a question by Billey, Fan and Losonczy. In other words, we show that Lehmer codes for type F₄ do not exist. Nevertheless, by introducing weak Lehmer codes, we construct explicitly multicomplexes and Lehmer complexes for any lower Bruhat interval in type F₄.

Citations

• The Lehmer complex of a Bruhat interval
• On the shape of Bruhat intervals

Cited by

• Billey-Postnikov posets, rationally smooth Schubert varieties, and Poincaré duality

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