From m-clusters to m-noncrossing partitions via exceptional sequences

Buan, Aslak Bakke; Reiten, Idun et Thomas, Hugh (2012). « From m-clusters to m-noncrossing partitions via exceptional sequences ». Mathematische Zeitschrift, 271(3-4), pp. 1117-1139.

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Résumé

Let W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number of noncrossing partitions for W. Natural bijections between these two sets are known. For any positive integer m, both m-clusters and m-noncrossing partitions have been defined, and the cardinality of both these sets is the Fuss–Catalan number Cm(W). We give a natural bijection between these two sets by first establishing a bijection between two particular sets of exceptional sequences in the bounded derived category Db(H) for any finite-dimensional hereditary algebra H.

Type: Article de revue scientifique
Mots-clés ou Sujets: exceptional objects, noncrossing partitions, clusters, derived categories, generalized Catalan numbers, hereditary algebras.
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Hugh R. Thomas
Date de dépôt: 18 mai 2016 19:49
Dernière modification: 30 mai 2016 20:12
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8482

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