Facets of the generalized cluster complex and regions in the extended Catalan arrangement of type \(A\)

zbMath1295.05045arXiv1302.2441MaRDI QIDQ396916

Eleni Tzanaki, Myrto Kallipoliti, Susanna Fishel

Publication date: 14 August 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2441

zbMATH Keywords

integer partitionscluster complexCatalan arrangements

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Elementary theory of partitions (11P81) Combinatorial aspects of simplicial complexes (05E45)

Related Items

Facets of the generalized cluster complex and regions in the extended Catalan arrangement of type \(A\) ⋮ Positive cluster complexes and τ-tilting simplicial complexes of cluster-tilted algebras of finite type ⋮ On floors and ceilings of the \(k\)-Catalan arrangement ⋮ Bijections between generalized Catalan families of types \(A\) and \(C\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Facets of the generalized cluster complex and regions in the extended Catalan arrangement of type \(A\)
• On noncrossing and nonnesting partitions of type \(D\)
• The number of intervals in the \(m\)-Tamari lattices
• The Kazhdan-Lusztig cells in certain affine Weyl groups
• Catalan numbers, their generalization, and their uses
• Maintaining the spirit of the reflection principle when the boundary has arbitrary integer slope
• \(Y\)-systems and generalized associahedra
• Polygon dissections and Euler, Fuss, Kirkman, and Cayley numbers
• Counting Shi regions with a fixed separating wall
• On the enumeration of positive cells in generalized cluster complexes and Catalan hyperplane arrangements.
• Cluster algebras I: Foundations
• A uniform bijection between nonnesting and noncrossing partitions
• A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path
• Clusters, Coxeter-sortable elements and noncrossing partitions
• Faces of Generalized Cluster Complexes and Noncrossing Partitions
• Alcoves Corresponding to an Affine Weyl Group
• On a refinement of the generalized Catalan numbers for Weyl groups
• GENERALIZED CATALAN NUMBERS, WEYL GROUPS AND ARRANGEMENTS OF HYPERPLANES
• Some decomposition numbers for Hecke algebras of general linear groups
• Hyperplane arrangements, interval orders, and trees.
• A bijection between noncrossing and nonnesting partitions of types A and B