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dc.contributor.authorMücksch, Paul
dc.contributor.authorRöhrle, Gerhard
dc.contributor.authorTran, Tan Nhat
dc.date.accessioned2023-02-13T11:27:04Z
dc.date.available2023-02-13T11:27:04Z
dc.date.issued2023-02-13
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4012
dc.description.abstractIn [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the property of accuracy stems from a flag of flats in the intersection lattice of the underlying arrangement. Members of this family are called flag-accurate. One relevance of this new notion is that it entails divisional freeness. There are a number of important natural classes which are flag-accurate, the most prominent one among them is the one consisting of Coxeter arrangements. This warrants a systematic study which is put forward in the present paper. More specifically, let $\mathscr A$ be a free arrangement of rank $\ell$. Suppose that for every $1\leq d \leq \ell$, the first $d$ exponents of $\mathscr A$ - when listed in increasing order - are realized as the exponents of a free restriction of $\mathscr A$ to some intersection of reflecting hyperplanes of $\mathscr A$ of dimension $d$. Following [MR21], we call such an arrangement $\mathscr A$ with this natural property accurate. If in addition the flats involved can be chosen to form a flag, we call $\mathscr A$ flag-accurate. We investigate flag-accuracy among reflection arrangements, extended Shi and extended Catalan arrangements, and further for various families of graphic and digraphic arrangements. We pursue these both from theoretical and computational perspectives. Along the way we present examples of accurate arrangements that are not flag-accurate. The main result of [MR21] shows that MAT-free arrangements are accurate. We provide strong evidence for the conjecture that MAT-freeness actually entails flag-accuracy.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2023-01
dc.subjectFree arrangementsen_US
dc.subjectReflection arrangementsen_US
dc.subjectCoxeter arrangementsen_US
dc.subjectIdeal arrangementsen_US
dc.subjectMAT-free arrangementsen_US
dc.subjectAccurate arrangementsen_US
dc.subjectExtended Catalan arrangementsen_US
dc.subjectExtended Shi arrangementsen_US
dc.subjectIdeal-Shi arrangementsen_US
dc.subjectGraphic arrangementsen_US
dc.subjectDigraphic arrangementsen_US
dc.titleFlag-Accurate Arrangementsen_US
dc.typePreprinten_US
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.identifier.doi10.14760/OWP-2023-01
local.scientificprogramOWLF 2022en_US
local.series.idOWP-2023-01en_US
local.subject.msc20en_US
local.subject.msc51en_US
local.subject.msc52en_US
local.subject.msc32en_US
dc.identifier.urnurn:nbn:de:101:1-2024032008555038657618
dc.identifier.ppn1838572015


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