By Shalosh B. Ekhad and Doron Zeilberger
Posted: Aug. 10, 2022
Abstract: This Maple package implements Allan Berele's constant-term expressions for certain Poincaré series called Cbar(n,k), described in his paper
Denominators for One Variable Poincaré series of generic matrices .
It arose in the theory of Polynomial Identity Rings and Invariant Theory, that thanks to Wilf-Zeilberger algorithmic proof theory can be used to derive linear recurrences for n=2 and n=3. This enables very fast computations of these series for many values of k. Alas, while the analogous recurrences exist for n=4 and above, finding them is currently beyond our meager computational powers.
Note: There is no accompanying article. Everything is contained in the Maple package and the output files.
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