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

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

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Electronic journal of combinatorics 2019-10, Vol.26 (4)
Hauptverfasser: Delucchi, Emanuele, Girard, Noriane, Paolini, Giovanni
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 4
container_start_page
container_title The Electronic journal of combinatorics
container_volume 26
creator Delucchi, Emanuele
Girard, Noriane
Paolini, Giovanni
description 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.
doi_str_mv 10.37236/7160
format Article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_37236_7160</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_37236_7160</sourcerecordid><originalsourceid>FETCH-LOGICAL-c221t-7bcff41370b4437aabc72afcf1556d8efd39b56da080f283a25274c54b2b196c3</originalsourceid><addsrcrecordid>eNpNkL1OwzAYRS0EEqXtO3hhDPgniZOxKj9FikRF2zn67HwGoyRGtpe8PSkwMN0zHN3hELLm7E4qIct7xUt2QRacKZVVtSgv__E1uYnxkzEu6rpYkNPhA_setOtdmqi3dO8jpnimBjT22NE9hOSS82OkMHZ0EwKM7zjgOGsPaN04O3qib94nephiwiGuyJWFPuL6b5fk9PR43O6y5vX5ZbtpMiMET5nSxtqcS8V0nksFoI0SYI3lRVF2FdpO1nomYBWzopIgCqFyU-RaaF6XRi7J7e-vCT7GgLb9Cm6AMLWctT8t2nML-Q2RWlEi</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems</title><source>DOAJ Directory of Open Access Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Delucchi, Emanuele ; Girard, Noriane ; Paolini, Giovanni</creator><creatorcontrib>Delucchi, Emanuele ; Girard, Noriane ; Paolini, Giovanni</creatorcontrib><description>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.</description><identifier>ISSN: 1077-8926</identifier><identifier>EISSN: 1077-8926</identifier><identifier>DOI: 10.37236/7160</identifier><language>eng</language><ispartof>The Electronic journal of combinatorics, 2019-10, Vol.26 (4)</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c221t-7bcff41370b4437aabc72afcf1556d8efd39b56da080f283a25274c54b2b196c3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,781,785,865,27929,27930</link.rule.ids></links><search><creatorcontrib>Delucchi, Emanuele</creatorcontrib><creatorcontrib>Girard, Noriane</creatorcontrib><creatorcontrib>Paolini, Giovanni</creatorcontrib><title>Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems</title><title>The Electronic journal of combinatorics</title><description>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.</description><issn>1077-8926</issn><issn>1077-8926</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNpNkL1OwzAYRS0EEqXtO3hhDPgniZOxKj9FikRF2zn67HwGoyRGtpe8PSkwMN0zHN3hELLm7E4qIct7xUt2QRacKZVVtSgv__E1uYnxkzEu6rpYkNPhA_setOtdmqi3dO8jpnimBjT22NE9hOSS82OkMHZ0EwKM7zjgOGsPaN04O3qib94nephiwiGuyJWFPuL6b5fk9PR43O6y5vX5ZbtpMiMET5nSxtqcS8V0nksFoI0SYI3lRVF2FdpO1nomYBWzopIgCqFyU-RaaF6XRi7J7e-vCT7GgLb9Cm6AMLWctT8t2nML-Q2RWlEi</recordid><startdate>20191011</startdate><enddate>20191011</enddate><creator>Delucchi, Emanuele</creator><creator>Girard, Noriane</creator><creator>Paolini, Giovanni</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191011</creationdate><title>Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems</title><author>Delucchi, Emanuele ; Girard, Noriane ; Paolini, Giovanni</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c221t-7bcff41370b4437aabc72afcf1556d8efd39b56da080f283a25274c54b2b196c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Delucchi, Emanuele</creatorcontrib><creatorcontrib>Girard, Noriane</creatorcontrib><creatorcontrib>Paolini, Giovanni</creatorcontrib><collection>CrossRef</collection><jtitle>The Electronic journal of combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Delucchi, Emanuele</au><au>Girard, Noriane</au><au>Paolini, Giovanni</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems</atitle><jtitle>The Electronic journal of combinatorics</jtitle><date>2019-10-11</date><risdate>2019</risdate><volume>26</volume><issue>4</issue><issn>1077-8926</issn><eissn>1077-8926</eissn><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.</abstract><doi>10.37236/7160</doi></addata></record>
fulltext fulltext
identifier ISSN: 1077-8926
ispartof The Electronic journal of combinatorics, 2019-10, Vol.26 (4)
issn 1077-8926
1077-8926
language eng
recordid cdi_crossref_primary_10_37236_7160
source DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
title Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-15T06%3A43%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Shellability%20of%20Posets%20of%20Labeled%20Partitions%20and%20Arrangements%20Defined%20by%20Root%20Systems&rft.jtitle=The%20Electronic%20journal%20of%20combinatorics&rft.au=Delucchi,%20Emanuele&rft.date=2019-10-11&rft.volume=26&rft.issue=4&rft.issn=1077-8926&rft.eissn=1077-8926&rft_id=info:doi/10.37236/7160&rft_dat=%3Ccrossref%3E10_37236_7160%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true