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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| Veröffentlicht in: | Journal of algebraic combinatorics 2025-02, Vol.61 (1), Article 8 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 0925-9899 1572-9192 |
| DOI: | 10.1007/s10801-024-01374-3 |