The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials

Masao Ishikawa, Jiang Zeng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 ( 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 languageEnglish
Title of host publicationFPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics
Pages490-499
Number of pages10
Publication statusPublished - 2006
Externally publishedYes
Event18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States
Duration: Jun 19 2006Jun 23 2006

Other

Other18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
CountryUnited States
CitySan Diego, CA
Period6/19/066/23/06

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Partition Function
Partition
Polynomial
Weighted Sums
Generating Function
Corollary
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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

Cite this

Ishikawa, M., & Zeng, J. (2006). The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials. In FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics (pp. 490-499)

The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials. / Ishikawa, Masao; Zeng, Jiang.

FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics. 2006. p. 490-499.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ishikawa, M & Zeng, J 2006, The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials. in FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics. pp. 490-499, 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006, San Diego, CA, United States, 6/19/06.
Ishikawa M, Zeng J. The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials. In FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics. 2006. p. 490-499
Ishikawa, Masao ; Zeng, Jiang. / The partition function of Andrews and Stanley and Al-Salam-Chihara polynomials. FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics. 2006. pp. 490-499
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