2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95871This is a complement to my previous article "Advanced Determinant Calculus" (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441-456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.AmS-LaTeX, 85 pages; Final, largely revised versionCombinatoricsMathematical PhysicsClassical Analysis and ODEsNumber TheoryRings and AlgebrasPrimary 05A19; Secondary 05A10 05A15 05A17 05A18 05A30 05E10 05E15 11B68 11B73 11C20 11Y60 15A15 33C45 33D45 33E05text