Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems

Delucchi, Emanuele and Girard, Noriane and Paolini, Giovanni (2019) Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems. The Electronic Journal of Combinatorics, 26 (4). ISSN 1077-8926

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Abstract

We prove that the posets of connected components of intersections of toric and elliptic arrangements defined by root systems are EL-shellable and we compute their homotopy type. Our method rests on Bibby's description of such posets by means of "labeled partitions": after giving an EL-labeling and counting homology chains for general posets of labeled partitions, we obtain the stated results by considering the appropriate subposets.

Item Type:	Scientific journal article, Newspaper article or Magazine article
Subjects:	Mathematical sciences
Department/unit:	Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sull'intelligenza artificiale
Depositing User:	Emanuele Delucchi
Date Deposited:	07 Jun 2022 09:21
Last Modified:	07 Jun 2022 09:22
URI:	http://repository.supsi.ch/id/eprint/13433

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