Chain decompositions of \(q, t\)-Catalan numbers via local chains

DOI10.1007/s00026-020-00512-5zbMath1460.05022arXiv2003.03896OpenAlexW3091605099MaRDI QIDQ2660062

Kyungyong Lee, Li Li, Nicholas A. Loehr, Seongjune Han

Publication date: 29 March 2021

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

Full work available at URL: https://arxiv.org/abs/2003.03896

zbMATH Keywords

integer partitionsDyck paths\(q,t\)-Catalan numberschain decompositionsjoint symmetrydinv statistic

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Elementary theory of partitions (11P81)

Related Items (1)

Chain decompositions of \(q, t\)-Catalan numbers: tail extensions and flagpole partitions

Cites Work

• Unnamed Item
• Rational parking functions and Catalan numbers
• Limits of modified higher \(q,t\)-Catalan numbers
• A continuous family of partition statistics equidistributed with length
• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• A combinatorial formula for the character of the diagonal coinvariants
• 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
• Combinatorics of certain higher \(q, t\)-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula
• A positivity result in the theory of Macdonald polynomials
• A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers
• A proof of the shuffle conjecture

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