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dc.contributor.authorStump, Christian
dc.contributor.authorThomas, Hugh
dc.contributor.authorWilliams, Nathan
dc.date.accessioned2019-01-21T07:49:47Z
dc.date.available2019-01-21T07:49:47Z
dc.date.issued2019-01-21
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1398
dc.description.abstractThe three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. We provide new viewpoints for both and introduce the missing generalization of sortable elements by lifting the theory from the Coxeter system to the associated positive Artin monoid. We show how this new perspective ties together all three generalizations, providing a uniform framework for noncrossing Fuß-Catalan combinatorics. Having developed the combinatorial theory, we provide an interpretation of our generalizations in the language of the representation theory of hereditary Artin algebras.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2019,01
dc.subjectCoxeter groupsen_US
dc.subjectArtin groupsen_US
dc.subjectCoxeter-Catalan combinatoricsen_US
dc.subjectFuß-Catalan numbersen_US
dc.subjectNoncrossing partitionsen_US
dc.subjectCluster complexesen_US
dc.subjectCoxeter-sortable elementsen_US
dc.subjectAssociahedraen_US
dc.subjectSubword complexesen_US
dc.titleCataland: Why the Fuß?en_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2019-01
local.scientificprogramResearch in Pairs 2018en_US
local.series.idOWP-2019-01en_US
local.subject.msc20en_US
local.subject.msc16en_US
local.subject.msc05en_US


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