Permutation statistics and the \(q,t\)-Catalan sequence

DOI10.1016/j.ejc.2004.01.006zbMath1056.05008OpenAlexW2083685161MaRDI QIDQ703606

Nicholas A. Loehr

Publication date: 11 January 2005

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2004.01.006

zbMATH Keywords

permutationsDyck pathsCatalan numbersmajor index statistics

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05)

Cites Work

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• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• A proof of the \(q,t\)-Catalan positivity conjecture
• Conjectured statistics for the \(q,t\)-Catalan numbers.
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• Two element lattice permutation numbers and their \(q\)-generalization
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• 𝑎𝑑-nilpotent 𝔟-ideals in 𝔰𝔩(𝔫) having a fixed class of nilpotence: combinatorics and enumeration
• Major Index and Inversion Number of Permutations
• On the Netto Inversion Number of a Sequence

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