A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers

DOI10.1137/16M1059916zbMath1386.05013arXiv1602.01126MaRDI QIDQ3130450

Kyungyong Lee, Li Li, Nicholas A. Loehr

Publication date: 22 January 2018

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

Full work available at URL: https://arxiv.org/abs/1602.01126

zbMATH Keywords

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

Mathematics Subject Classification ID

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

Related Items (3)

Chain decompositions of \(q, t\)-Catalan numbers via local chains ⋮ Chain decompositions of \(q, t\)-Catalan numbers: tail extensions and flagpole partitions ⋮ Generalized \(q,t\)-Catalan numbers

Uses Software

• SageMath

Cites Work

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• A combinatorial approach to the \(q,t\)-symmetry relation in Macdonald polynomials
• Limits of modified higher \(q,t\)-Catalan numbers
• New combinatorial formulations of the shuffle conjecture
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• Compactified Jacobians and \(q,t\)-Catalan numbers. I.
• A combinatorial formula for the character of the diagonal coinvariants
• Conjectured statistics for the higher \(q,t\)-Catalan sequences
• Combinatorics of \(q\), \(t\)-parking functions
• 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
• A bijective proof of a factorization formula for specialized Macdonald polynomials
• Combinatorics of certain higher \(q, t\)-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula
• Compactified Jacobians and \(q,t\)-Catalan numbers. II
• A positivity result in the theory of Macdonald polynomials
• A combinatorial formula for Macdonald polynomials
• Combinatorics, Second Edition
• A combinatorial model for the Macdonald polynomials

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