Français
Functional equations and combinatorics
Multi angle
Authors : Di Vizio, Lucia (Author of the conference)
CIRM (Publisher )
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}
Additional resources :
https://www.cirm-math.fr/RepOrga/3047/Slides/2024-JNCF-II-handout.pdf
CIRM (Publisher )
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Abstract :
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.
Keywords : 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
MSC Codes : Keywords : 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}
Additional resources :
https://www.cirm-math.fr/RepOrga/3047/Slides/2024-JNCF-II-handout.pdf
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 25/03/2024 Conference Date : 07/03/2024 Subseries : Research School arXiv category : Combinatorics ; Number Theory Mathematical Area(s) : Combinatorics ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:24:44 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-03-07_Di_Visio_3_2.mp4 
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Information on the Event
Event Title : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formelEvent Organizers : Berthomieu, Jérémy ; Bréhard, Florent ; Maignan, Aude ; Mohammadi, Fatemeh ; Ollivier, François Dates : 04/03/2024 - 08/03/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3047.html
Citation Data
DOI : 10.24350/CIRM.V.20149203Cite this video as: 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 |
See Also
- [Multi angle] Designing and exploiting fast algorithms for univariate polynomial matrices - Lecture 2 / Author of the conference Neiger, Vincent.
- [Multi angle] Creative telescoping for D-finite functions - Lecture 2 / Author of the conference Koutschan, Christoph.
- [Multi angle] Algebraic attacks for the rank decoding problem - Lecture 2 / Author of the conference Bardet, Magali.
- [Multi angle] Designing and exploiting fast algorithms for univariate polynomial matrices - Lecture 1 / Author of the conference Neiger, Vincent.
- [Multi angle] Creative telescoping for D-finite functions - Lecture 1 / Author of the conference Koutschan, Christoph.
- [Multi angle] Algebraic attacks for the rank decoding problem - Lecture 1 / Author of the conference Bardet, Magali.
Bibliography
- 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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