The rank enumeration of certain parabolic non-crossing partitions

DOI10.5802/alco.219zbMath1492.05011arXiv1910.13244OpenAlexW2982342079MaRDI QIDQ2152767

Henri Mühle, Christian Krattenthaler

Publication date: 11 July 2022

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.13244

zbMATH Keywords

generating functionDyck pathLagrange inversionnon-crossing partitionballot pathzeta polynomial

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Partitions of sets (05A18) Combinatorics of partially ordered sets (06A07)

Related Items (5)

Hochschild lattices and shuffle lattices ⋮ $F$- and $H$-triangles for $\nu$-associahedra ⋮ \(F\)- and \(H\)-triangles for \(\nu \)-associahedra ⋮ Refined lattice path enumeration and combinatorial reciprocity ⋮ Parabolic Tamari lattices in linear type \(B\)

Cites Work

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• Enumeration of chains and saturated chains in Dyck lattices.
• SB-lattices, distributivity, and Bruhat order on sortable elements.
• On some enumerative aspects of generalized associahedra
• Intervals in Catalan lattices and realizers of triangulations
• Chain enumeration and non-crossing partitions
• Multichains, non-crossing partitions and trees
• On the structure of the lattice of noncrossing partitions
• Chains in the lattice of noncrossing partitions
• Some properties of crossings and partitions
• Non-crossing partitions for classical reflection groups
• Enumerative properties of generalized associahedra
• Noncrossing arc diagrams, Tamari lattices, and parabolic quotients of the symmetric group
• Chapoton triangles for nonkissing complexes
• Tamari lattices for parabolic quotients of the symmetric group
• \texttt{Findstat} -- a database and search engine for combinatorial statistics and maps
• Ballot-noncrossing partitions
• On the number of full reflections in finite Coxeter groups.
• A Heyting algebra on Dyck paths of type \(A\) and \(B\)
• Cyclic sieving phenomena on annular noncrossing permutations
• On the \(H\)-triangle of generalised nonnesting partitions
• A distributive lattice structure connecting Dyck paths, noncrossing partitions and 312-avoiding permutations
• Sur les partitions non croisées d'un cycle. (The non-crossed partitions of a cycle)
• The \(M\)-triangle of generalised non-crossing partitions for the types \(E_7\) and \(E_8\).
• Lattice Path Enumeration
• The dual braid monoid
• Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions
• Faces of Generalized Cluster Complexes and Noncrossing Partitions
• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Noncrossing Partitions for the GroupDn
• On a refinement of the generalized Catalan numbers for Weyl groups
• Non-crossing partition lattices in finite real reflection groups
• A partial order on the symmetric group and new \(K(\pi,1)\)'s for the braid groups

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