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

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

2005-06-08

arxiv.org/abs/math/0506128v2

Mathematics

Combinatorics

25 pages

Scientific paper

We show that the sum of the four parameter weights over all ordinary or strict partitions with parts each less than or equal to a given integer $N$ is expressed by the Al-Salam Chihara polynomials. This weight is a generalization of the Andrews-Stanley partition function. As a corollary we prove C. Boulet's results when the sum runs over all ordinary or strict partitions. In the last section we study the weighted sum of Schur's $P$-functions and $Q$-functions, where the sum runs over all strict partitions.

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