dc.contributor.author
Cuntz, Michael
dc.contributor.author
Elia, Sophia
dc.contributor.author
Labbé, Jean-Philippe
dc.date.accessioned
2022-05-02T06:49:42Z
dc.date.available
2022-05-02T06:49:42Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/32956
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-32682
dc.description.abstract
A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter arrangements and also the weak order through the poset of regions. The weak order is known to be a congruence normal lattice, and congruence normality of lattices of regions of simplicial arrangements can be determined using polyhedral cones called shards. In this article, we update Grünbaum’s catalogue by providing normals realizing all known simplicial arrangements with up to 37 lines and key invariants. Then we add structure to this catalogue by determining which arrangements always/sometimes/never lead to congruence normal lattices of regions. To this end, we use oriented matroids to recast shards as covectors to determine congruence normality of large hyperplane arrangements. We also show that lattices of regions coming from finite Weyl groupoids of any rank are always congruence normal.
en
dc.format.extent
85 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Simplicial hyperplane arrangements
en
dc.subject
Poset of regions
en
dc.subject
Congruence normality and uniformity
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.doi
10.1007/s00026-021-00555-2
dcterms.bibliographicCitation.journaltitle
Annals of Combinatorics
dcterms.bibliographicCitation.number
1
dcterms.bibliographicCitation.pagestart
1
dcterms.bibliographicCitation.pageend
85
dcterms.bibliographicCitation.volume
26
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s00026-021-00555-2
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
0219-3094
refubium.resourceType.provider
WoS-Alert