Tewodros Amdeberhan, Christoph Koutschan, Doron Zeilberger
Published 2023-07-04Version 1
In this {\it case study}, we hope to show why Sheldon Axler was not just wrong, but {\em wrong}, when he urged, in 1995: ``Down with Determinants!''. We first recall how determinants are useful in enumerative combinatorics, and then illustrate three versatile tools (Dodgson's condensation, the holonomic ansatz and constant term evaluations) to operate in tandem to prove a certain intriguing determinantal formula conjectured by the first author.
Arithmetic of Some Sequences Via $2$-determinants
On a class of determinants
Determinants of Box Products of Paths
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