Yay for Determinants!
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Publication:6442611
arXiv2307.01912MaRDI QIDQ6442611
Doron Zeilberger, Christoph Koutschan, Tewodoros Amdeberhane
Publication date: 4 July 2023
Abstract: 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. We conclude with a postscript describing yet another, much more efficient, method 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.
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