Mathematics Colloquia and Seminars

In enumerative combinatorics, the bijective approach has proved extremely successful in studying diverse combinatorial objects, such as trees, partitions, Young tableaux, etc. However, in the last two decades, a number of probabilistic algorithms for random generation revealed a new and often unexpected side of these classical objects. In the first half of the talk, we present a brief survey of the probabilistic random generation, together with some applications. In the second half of the talk, we introduce a new weighted hook walk giving an interesting (non-uniform) distribution on standard Young tableaux. We then show how to go back and obtain a new short bijective proof of the hook-length formula. This is a joint work with Ionut Ciocan-Fontanine and Matjaz Konvalinka. The talk will be accessible to a general audience, so no background in combinatorics is assumed.