Le Séminaire de Combinatoire Enumérative et Analytique, également appelé Séminaire Philippe Flajolet depuis 2011, a pour objectif de couvrir un large spectre de recherche en combinatoire, et est ouvert à tou·te·s les chercheur·se·s et étudiant·e·s intéressé·e·s.
Le séminaire a lieu à l’IHP en salle Yvette Cauchois (bâtiment Perrin, second étage).
Prochaine séance : Jeudi 5 juin 2025
Nous écouterons
- 11h: Florent Koechlin (LIPN, Paris Nord),
Generating Functions and Ambiguity in Automata TheoryIn the 1980s, Philippe Flajolet elegantly resolved several conjectures on the inherent ambiguity of some context-free languages. The tools he developed rely on the study of the nature of the generating functions associated with these languages, specifically their algebraicity. In this talk, I will present an extension of this approach to a broader class of languages, recognized by Parikh (pushdown) automata.
- 14h: Sophie Morier-Genoud (LMR, Université Reims Champagne-Ardenne),
An overview of q-analogs of real numbers
Many classical sequences of integers have well established q-analogs. The most fundamental ones are certainly the q-integers and the q-binomial coefficients which both appear in various areas of mathematics and physics. With Valentin Ovsienko we recently suggested a definition for the q-rational numbers based on combinatorial properties and on continued fraction expansions. The definition of q-rationals naturally extends the one of q-integers and leads to a ratio of polynomials with positive integer coefficients. A surprising phenomenon of stabilization allows us to define q-irrational numbers as formal power series with integer coefficients. These q-numbers have been studied in connection with many fields such as combinatorics of posets, braid groups and knots invariants, homological algebra, Markov-Hurwitz approximation, cluster algebras. In this talk I will give an overview of the subject. I will recall the basic definitions and properties and present new symmetries on the q-reals.
- 15h: Mohab Safey El Din (LIP6, Sorbonne Université),
Computer algebra tools for solving combinatorial functional equationsFollowing Flajolet's recipe to solve counting problems in enumerative combinatorics through generating functions, one is often led to refine the initial enumeration by introducing catalytic variables and to write functional equations of fixed-point type, called Discrete Differential Equations. A celebrated result by Bousquet-Mélou and Jehanne is that solutions to these equations are algebraic, i.e. they are annihilated by a non-zero polynomial. In this talk, I will show how to use computer algebra tools to compute such polynomial annihilators and will present recent applications due to Bousquet-Mélou and Notarantonio. This talk is based on joint works with Alin Bostan and Hadrien Notarantonio.
Liste des séances de l’année
Les séances de l’année 2024-2025 ont lieu :
-
- jeudi 10 octobre 2024
- Nicolas Broutin
- Marthe Bonamy
- Florent Hivert
- jeudi 05 décembre 2024
- Bram Petri
- Eleanor Archer
- Frédéric Chapoton
- jeudi 06 février 2025
- Baptiste Louf
- Adeline Pierrot
- Thomas Dreyfus
- jeudi 03 avril 2025
- Pierre Tarrago
- Sofia Tarricone
- Wenjie Fang
- jeudi 05 juin 2025
- Florent Koechlin
- Sophie Morier-Genoud
- Mohab Safey El Din
- jeudi 10 octobre 2024