Résumé : There are a number of combinatorial structures that admit a notion of irreducibility in some sense, including connected graphs and surfaces, irreducible tournaments and indecomposable permutations. We are interested in the asymptotic behaviour of probability that a random labelled object is irreducible, as its size tends to infinity. It turns out that, under some conditions, it is possible to obtain this asymptotics with the help of the symbolic method. Namely, it is so when the considered combinatorial class can be described as a set or a sequence of the corresponding irreducible class, and when its counting sequence grows sufficiently fast. Moreover, the coefficients involved in the asymptotic expansion are often integers. We explain their combinatorial meaning. This is an ongoing joint work with Thierry Monteil.
Dernière modification : Wednesday 23 September 2020 | Contact : Cyril.Banderier at lipn.univ-paris13.fr |