Le Séminaire de Combinatoire Enumérative et Analytique, rebaptisé Séminaire Philippe Flajolet le 7 avril 2011, a pour objectif de couvrir un large spectre de recherche en combinatoire, et est ouvert à tous les chercheurs et étudiants intéressés.

Il se tient un jeudi tous les deux mois à l'IHP, plus de détails ici.

Les séances de l'année 2017 - 2018 auront lieu :

  • jeudi 21 septembre 2017 - IHP, Amphi Hermite
  • jeudi 7 décembre 2017 - IHP, Amphi Hermite
  • jeudi 15 février 2018 - IHP, Amphi Hermite
  • jeudi 12 avril 2018 - IHP, Amphi Hermite
  • jeudi 7 juin 2018 - IHP, Amphi Darboux


Prochaine séance : jeudi 7 juin 2018, Amphi Darboux, IHP
  • 13h45 - 14h45 : Matjaz Konvalinka (Université de Ljubljana),
    Smirnov words, Smirnov trees, and e-positivity,
    .

A word is called Smirnov if adjacent letters are distinct. It is known that the generating function for Smirnov words is e-positive, i.e. it can be expressed as a linear combination of elementary symmetric functions with non-negative integer coefficients. We will define Smirnov trees and prove, via a bijection, that their generating function is also e-positive.
This is joint work with Vasu Tewari.

  • 14h45 - 15h45 : Vlady Ravelomanana (IRIF, Paris 7),
    Combinatorics of some tractable phase transitions,
    .

Several combinatorial structures are subject to phase transitions as one of their parameters increases when their sizes are large but fixed. Such structures include random CNF formulas (a SAT/UNSAT transition occurs from under to overconstrained instances) or random graphs (from sparse to dense instances some properties vanish).
Determining the nature of a phase transition (sharp or coarse), locating it, determining a precise scaling window and better understanding the structure of the space of solutions turn out to be very interesting tasks. These challenges have aroused a lot of interest in different communities, namely mathematics, computer science and physics.
In this talk, we will review various phase transitions of random graph properties or $2$-CNF formulas, emphasizing the strengths (and limits?) of enumerative/analytic approaches.