The q, t-symmetry of the generalized q, t-Catalan number C(k1,k2,k3)(q,t)

We present two distinct proofs of the q ,  t -symmetry for the generalized q ,  t -Catalan number C k → ( q , t ) , where k → = ( k 1 , k 2 , k 3 ) . The first proof is derived through the application of MacMahon’s partition analysis. The second proof is established via a direct bijection.

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2025-02, Vol.61 (1), p.8, Article 8
Main Authors: Xin, Guoce, Zhang, Yingrui
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Numbers
Order
Ordered Algebraic Structures
Symmetry
Variables
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