Inductive and divisional posets

verfasst von

Roberto Pagaria, Tan Nhat Tran, Maddalena Pismataro , Lorenzo Vecchi

Abstract

We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass of divisional posets. It then motivates us to define the so-called inductive and divisional abelian (Lie group) arrangements, whose posets of layers serve as the main examples of our posets. Our first main result is that every divisional poset is factorable. Our second main result shows that the class of inductive posets contains strictly supersolvable posets, the notion recently introduced due to Bibby and Delucchi (2022). This result can be regarded as an extension of a classical result due to Jambu and Terao (Adv. in Math. 52 (1984) 248–258), which asserts that every supersolvable hyperplane arrangement is inductively free. Our third main result is an application to toric arrangements, which states that the toric arrangement defined by an arbitrary ideal of a root system of type (Formula presented.), (Formula presented.) or (Formula presented.) with respect to the root lattice is inductive.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Università di Bologna

Typ

Artikel

Journal

Journal of the London Mathematical Society

Band

109

ISSN

0024-6107

Publikationsdatum

20.12.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.1112/jlms.12829 (Zugang: Offen)