2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79259Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all coincide with the classical version. In this way, we get some new q-tangent and q-secant functions. Some of them also have nice continued fraction expansions; in one particular case, we could not find a proof for it. Divisibility results a la Andrews/Foata/Gessel are also discussed.If you want to see more of my papers, go here: http://www.wits.ac.za/helmut/paperlst.htmCombinatorics05A15text