Part II of Computing Determinants Involving Stirling Numbers Tewodros AMDEBERHAN and Shalosh B. EKHAD

Using the Jacobi-Trudi formula mentioned in Theorem 2 in Part I (Eq. (I.3.5) in [M], p.4.1) we computed explicit expressions for β_{n}(a, b), as well as the explicit generating functions ∑_{n=0}^{∞} β_{n}(a, b)q^{n} (that are always rational functions of q). for all 10 ≥ n ≥ a ≥ b ≥ 0. The output file is

https://sites.math.rutgers.edu/~zeilberg/tokhniot/oStirlingDet1.txt .

It was generated by executing the command

Paper1(10,n,q):

in the Maple package accompanying this article, that can be gotten from.

https://sites.math.rutgers.edu/~zeilberg/tokhniot/StirlingDet.txt .

References

[M] Ian G. Macdonald, “Symmetric Functions and Hall Polynomials”, second edition, Clarendon Press, Oxford, 1995.

Shalosh B. Ekhad, c/o D. Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA.

Email: ShaloshBEkhad at gmail dot com .

Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA.

Email: DoronZeil at gmail dot com .