Shellability of generalized Dowling posets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:171

Article

Paolini, Giovanni¹ 

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy

关键词: Shellability;    Configuration spaces;    Posets;    Dowling lattices;   

DOI  :  10.1016/j.jcta.2019.105159

来源: Elsevier

【 摘 要 】

A generalization of Dowling lattices was recently introduced by Bibby and Gadish, in a work on orbit configuration spaces. The authors left open the question as to whether these posets are shellable. In this paper we prove EL-shellability and use it to determine the homotopy type. Our result generalizes shellability of Dowling lattices and of posets of layers of abelian arrangements defined by root systems. We also show that subposets corresponding to invariant subarrangements are not shellable in general. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free