English
Functional equations and combinatorics
Multi angle
Auteurs : Di Vizio, Lucia (Auteur de la conférence)
CIRM (Editeur )
05A15 - Exact enumeration problems, generating functions
05A40 - Umbral calculus
11B68 - Bernoulli and Euler numbers and polynomials
12H05 - Differential algebra
30D30 - Meromorphic functions, general theory
33B15 - Gamma, beta and polygamma functions
33C45 - Orthogonal polynomials and functions (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.)
39A10 - Difference equations, See also {33Dxx}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3047/Slides/2024-JNCF-II-handout.pdf
CIRM (Editeur )
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Résumé :
Starting from a presentation of the many recent applications of Galois theory of functional equations to enumerative combinatorics, we will introduce the Galois theory of (different kinds) of difference equations. We will focus on the point of view of the applications, hence with little emphasis on the technicalities of the domain, but I'm willing to do an hour of « exercises » (i.e. to go a little deeper into the proofs), if a part of the audience is interested.
Mots-Clés : D-finite; differential Galois theory; iterative equation; generating function; self-similar graphs; complete trees; pattern avoiding permutation; Combinatorial power series; differential transcendence; Sheffer sequences; Bell numbers; Bernoulli numbers; Euler numbers; Genocchi numbers
Codes MSC : Mots-Clés : D-finite; differential Galois theory; iterative equation; generating function; self-similar graphs; complete trees; pattern avoiding permutation; Combinatorial power series; differential transcendence; Sheffer sequences; Bell numbers; Bernoulli numbers; Euler numbers; Genocchi numbers
05A15 - Exact enumeration problems, generating functions
05A40 - Umbral calculus
11B68 - Bernoulli and Euler numbers and polynomials
12H05 - Differential algebra
30D30 - Meromorphic functions, general theory
33B15 - Gamma, beta and polygamma functions
33C45 - Orthogonal polynomials and functions (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.)
39A10 - Difference equations, See also {33Dxx}
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3047/Slides/2024-JNCF-II-handout.pdf
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de Publication : 25/03/2024 Date de Captation : 07/03/2024 Sous Collection : Research School Catégorie arXiv : Combinatorics ; Number Theory Domaine(s) : Combinatoires ; Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 01:24:44 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-03-07_Di_Visio_3_2.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formelOrganisateurs de la Rencontre : Berthomieu, Jérémy ; Bréhard, Florent ; Maignan, Aude ; Mohammadi, Fatemeh ; Ollivier, François Dates : 04/03/2024 - 08/03/2024 Année de la rencontre : 2024 URL de la Rencontre : https://conferences.cirm-math.fr/3047.html
Données de citation
DOI : 10.24350/CIRM.V.20149203Citer cette vidéo: Di Vizio, Lucia (2024). Functional equations and combinatorics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20149203 URI : http://dx.doi.org/10.24350/CIRM.V.20149203 |
Voir Aussi
- [Multi angle] Designing and exploiting fast algorithms for univariate polynomial matrices - Lecture 2 / Auteur de la conférence Neiger, Vincent.
- [Multi angle] Creative telescoping for D-finite functions - Lecture 2 / Auteur de la conférence Koutschan, Christoph.
- [Multi angle] Algebraic attacks for the rank decoding problem - Lecture 2 / Auteur de la conférence Bardet, Magali.
- [Multi angle] Designing and exploiting fast algorithms for univariate polynomial matrices - Lecture 1 / Auteur de la conférence Neiger, Vincent.
- [Multi angle] Creative telescoping for D-finite functions - Lecture 1 / Auteur de la conférence Koutschan, Christoph.
- [Multi angle] Algebraic attacks for the rank decoding problem - Lecture 1 / Auteur de la conférence Bardet, Magali.
Bibliographie
- BOSTAN, Alin, DI VIZIO, Lucia, et RASCHEL, Kilian. Differential transcendence of Bell numbers and relatives: a Galois theoretic approach. arXiv preprint arXiv:2012.15292, 2020. - https://doi.org/10.48550/arXiv.2012.15292
- DI VIZIO, Lucia, FERNANDES, Gwladys, et MISHNA, Marni. Inhomogeneous order 1 iterative functional equations with applications to combinatorics. arXiv preprint arXiv:2309.07680, 2023. - https://doi.org/10.48550/arXiv.2309.07680
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