On \({\boldsymbol q}\)-Counting of Noncrossing Chains and Parking Functions

DOI10.1137/23m1572386arXiv2312.07351OpenAlexW4392461275MaRDI QIDQ6195953

Yen-Jen Cheng, Jyun-Cheng Yao, Tung-Shan Fu, Sen-Peng Eu

Publication date: 14 March 2024

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

Full work available at URL: https://arxiv.org/abs/2312.07351

zbMATH Keywords

Coxeter groupnoncrossing partitionparking functionsabsolute order

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Combinatorial aspects of groups and algebras (05E16)

Cites Work

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• On non-conjugate Coxeter elements in well-generated reflection groups
• A refinement of Cayley's formula for trees
• Refined enumeration of noncrossing chains and hook formulas
• Fibonacci polynomials and Sylvester determinant of tridiagonal matrix
• A simple bijection for the regions of the Shi arrangement of hyperplanes
• Some properties of crossings and partitions
• Non-crossing partitions for classical reflection groups
• Parking functions and noncrossing partitions
• Parking functions of types A and B
• Enumerative properties of generalized associahedra
• \(K(\pi,1)\)'s for Artin groups of finite type.
• Counting chains in the noncrossing partition lattice via the \(W\)-Laplacian
• Noncrossing partitions, Bruhat order and the cluster complex
• The Shi arrangement and the Ish arrangement
• Combinatorics of Coxeter Groups
• The dual braid monoid
• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Minimal factorizations of a cycle: a multivariate generating function
• Non-crossing partition lattices in finite real reflection groups

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