Séminaire Lotharingien de Combinatoire, B89a (2023), 14 pp.
A Case Study in Determinant Evaluations
Tewodros Amdeberhan, Christoph Koutschan and Doron Zeilberger
Abstract.
In this case study, we hope to elucidate three versatile and
powerful tools (Dodgson's condensation, the holonomic ansatz and
constant term evaluations) to operate in tandem in proving a certain
determinantal formula conjectured by the first author.
We also include a postscript describing yet another, more
methodological, toolbox for evaluating determinants: `ask
determinant-guru, Christian Krattenthaler', but advise people
only to use it as a last resort, since if we would have used this last
method right away, we would not have had the fun of doing it all by
ourselves. Throughout this paper, the reader finds new proofs of
interest while marching along the untrodden ways of our journey.
Received: July 22, 2023.
Revised: August 14, 2023.
Accepted: August 15, 2023.
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