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.
The input file generates the output file
The input file generates the output file
The input file generates the output file
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