A combinatorial proof of the parity unimodality of the \((m,n)\)-rational \(q\)-Catalan polynomial for \(m=3\)

DOI10.1016/j.amc.2022.127616OpenAlexW4308159272WikidataQ115222192 ScholiaQ115222192MaRDI QIDQ2101912

Yanyan Li

Publication date: 7 December 2022

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2022.127616

zbMATH Keywords

posetsunimodal sequenceschain decompositionsrational \(q\)-Catalan polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17)

Cites Work

• Unnamed Item
• Rational parking functions and Catalan numbers
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• The \(q\)-log-concavity and unimodality of \(q\)-Kaplansky numbers
• On parity unimodality of \(q\)-Catalan polynomials
• A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path
• The limiting distribution of the coefficients of the 𝑞-Catalan numbers
• A proof of the shuffle conjecture
• Algebraic Combinatorics
• Parity-Unimodality and a Cyclic Sieving Phenomenon for Necklaces

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