Chains in the Noncrossing Partition Lattice

DOI10.1137/07069777XzbMath1168.05008arXiv0706.2778MaRDI QIDQ3393423

Nathan Reading

Publication date: 20 August 2009

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.2778

zbMATH Keywords

Catalan numberCoxeter groupparking functionnoncrossing partitionabsolute orderCoxeter elementgeneralized cluster complexchain enumeration

Mathematics Subject Classification ID

Partitions of sets (05A18) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (16)

Counting chains in the noncrossing partition lattice via the \(W\)-Laplacian ⋮ The Catalan combinatorics of the hereditary artin algebras ⋮ Symmetric decompositions and the strong Sperner property for noncrossing partition lattices ⋮ Counting factorizations of Coxeter elements into products of reflections ⋮ Refined enumeration of noncrossing chains and hook formulas ⋮ The action of a Coxeter element on an affine root system ⋮ Coxeter factorizations and the matrix tree theorem with generalized Jucys-Murphy weights ⋮ SB-lattices, distributivity, and Bruhat order on sortable elements. ⋮ Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions ⋮ Hurwitz orbits of primitive factorizations of a Coxeter element. ⋮ Noncrossing partitions and the shard intersection order ⋮ Lyashko-Looijenga morphisms and submaximal factorizations of a Coxeter element ⋮ On enumerating factorizations in reflection groups ⋮ Unnamed Item ⋮ Tamari lattices for parabolic quotients of the symmetric group ⋮ A generalization of Euler numbers to finite Coxeter groups

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