Some recent results in enumerative and bijective combinatorics

The first part of the talk discusses a generating functions approach to the analysis of Grand Averages of some characteristic parameters of multiple Quickselect (Hoare's Find algorithm for several elements). With this new approach, it is possible for the first time to compute the variances. This research is quite recent and extends previous results that were presented in the algorithms seminar some time ago. In the second part, three simple bijections will be described, explaining combinatorially several formul\ae \ of Barcucci, Moon, and others.