Abstract
For any partition λ let ω(λ) denote the four parameter weight (equation presented) and let ℓ(λ) be the length of λ. We show that the generating function Σω(λ)z ℓ( λ), where the sum runs over all ordinary (resp. strict) partitions with parts each ≤ N, can be expressed by the Al-Salam-Chihara polynomials. As a corollary we prove G.E. Andrews' result by specializing some parameters and C. Boulet's results when N → +∞. In the last section we study the weighted sum Σω(λ)z ℓ(λ)P λ(x) where P λ(x) is Schur's P-function and the sum runs over all strict partitions.
| Original language | English |
|---|---|
| Pages | 490-499 |
| Number of pages | 10 |
| Publication status | Published - Dec 1 2006 |
| Externally published | Yes |
| Event | 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States Duration: Jun 19 2006 → Jun 23 2006 |
Other
| Other | 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 |
|---|---|
| Country/Territory | United States |
| City | San Diego, CA |
| Period | 6/19/06 → 6/23/06 |
Keywords
- Al-Salam-Chihara polynomials
- Basic hypergeometric functions
- Minor summation formula of Pfaffians
- Partitions
- Pfaffians
- Schur's Q-functions
- Symmetric functions
ASJC Scopus subject areas
- Algebra and Number Theory