Résumé : A pattern in a permutation is a subsequence with a specific relative order. What can we say about a typical large random permutation that avoids a particular pattern? We use a variety of approaches. For certain classes we give a geometric description that relates these classes to other types of well-studied random objects like random walks or random trees. Using the right geometric description we can find the the distribution of certain statistics like the number and location of fixed points. Earlier work dealt with permutations that avoid a pattern of length 3 using a variety of bijections. More recently, using connections with random walks in cones, we show certain scaling limits for permutations avoiding longer monotone patterns are given by traceless Dyson Brownian motion. This is joint work with Christopher Hoffman and Douglas Rizzolo.
Dernière modification : Tuesday 02 October 2018 | Contact : Cyril.Banderier at lipn.univ-paris13.fr |