Combinatorial statistics on non-crossing partitions

DOI10.1016/0097-3165(94)90066-3zbMath0803.05003OpenAlexW2171022442MaRDI QIDQ1328401

Rodica Simion

Publication date: 4 July 1994

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(94)90066-3

zbMATH Keywords

permutation statisticsstatisticsCatalan numbersNarayana numbersset partitionnon-crossing partitionsYoung's lattice

Mathematics Subject Classification ID

Partitions of sets (05A18)

Related Items (34)

Two injective proofs of a conjecture of Simion. ⋮ Counting occurrences of subword patterns in non-crossing partitions ⋮ Interpolating set partition statistics ⋮ Refined Catalan and Narayana cyclic sieving ⋮ Two combinatorial statistics on Dyck paths ⋮ On \(q\)-analogues of partially ordered sets ⋮ New refined enumerations of set partitions related to sorting ⋮ Restricted growth function patterns and statistics ⋮ Set Partition Patterns and the Dimension Index ⋮ Non-crossing partitions for classical reflection groups ⋮ Area of Catalan paths on a checkerboard ⋮ Octabasic Laguerre polynomials and permutation statistics ⋮ From G-parking functions to B-parking functions ⋮ On trees and noncrossing partitions ⋮ Juggling and applications to \(q\)-analogues ⋮ Revstack sort, zigzag patterns, descent polynomials of \(t\)-revstack sortable permutations, and Steingrímsson's sorting conjecture ⋮ Merging-Free Partitions and Run-Sorted Permutations ⋮ On noncrossing and nonnesting partitions of type \(D\) ⋮ Counting pattern-free set partitions. I: A generalization of Stirling numbers of the second kind ⋮ Weighted-inversion statistics and their symmetry groups ⋮ Counting water cells in bargraphs of compositions and set partitions ⋮ Actions on permutations and unimodality of descent polynomials ⋮ On 1212-avoiding restricted growth functions ⋮ A simple and direct derivation for the number of noncrossing partitions ⋮ Some open questions about random walks, involutions, limiting distributions, and generating functions ⋮ Set partition statistics and \(q\)-Fibonacci numbers ⋮ Ascending runs in permutations and valued Dyck paths ⋮ THE COMBINATORICS OF THE r-FREE CONVOLUTION ⋮ \(q\)-Narayana numbers and the flag \(h\)-vector of \(J(\text \textbf{2}\times {\mathbf n})\) ⋮ Visibility in non-crossing and non-nesting partitions ⋮ Dyck path enumeration ⋮ Log concavity of a sequence in a conjecture of Simion ⋮ A simple proof of a conjecture of Simion ⋮ Multiplicative functions on the lattice of non-crossing partitions and free convolution

Cites Work

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• \(p,q\)-Stirling numbers and set partition statistics
• q-Catalan numbers
• Q-counting rook configurations and a formula of Frobenius
• Catalan numbers, \(q\)-Catalan numbers and hypergeometric series
• Chain enumeration and non-crossing partitions
• Restricted growth functions, rank row matchings of partition lattices, and q-Stirling numbers
• Multichains, non-crossing partitions and trees
• On the structure of the lattice of noncrossing partitions
• Chains in the lattice of noncrossing partitions
• The q-Stirling numbers of first and second kinds
• Sur les partitions non croisées d'un cycle. (The non-crossed partitions of a cycle)
• Denert's Permutation Statistic Is Indeed Euler‐Mahonian
• Restricted permutations

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