English
Algorithmic methods for enumerative combinatorics - lecture 1
Multi angle
Auteurs : Koutschan, Christoph (Auteur de la conférence)
CIRM (Editeur )
05A19 - Combinatorial identities, bijective combinatorics
05A20 - Combinatorial inequalities
68W30 - Symbolic computation and algebraic computation
47L20 - Operator ideals
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3341/Slides/cours-koutschan-final.pdf
CIRM (Editeur )
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Résumé :
We showcase several algorithmic methods that can assist in solving combinatorial problems. Such algorithms include recurrence guessing, closure properties for D-finite functions, creative telescoping, or cylindrical algebraic decomposition, which are implemented in many today's computer algebra systems. We demonstrate with numerous examples how these can be applied beneficially in the context of enumerative combinatorics.
Mots-Clés : cylindrical algebraic decomposition; CAD; lattice reduction; LLL; recurrence guessing; D-finite function; creative telescoping
Codes MSC : Mots-Clés : cylindrical algebraic decomposition; CAD; lattice reduction; LLL; recurrence guessing; D-finite function; creative telescoping
05A19 - Combinatorial identities, bijective combinatorics
05A20 - Combinatorial inequalities
68W30 - Symbolic computation and algebraic computation
47L20 - Operator ideals
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3341/Slides/cours-koutschan-final.pdf
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Informations sur la Vidéo
Réalisateur : Récanzone, LucaLangue : Anglais Date de Publication : 00/00/0000 Date de Captation : 17/03/2025 Sous Collection : Research School Catégorie arXiv : Combinatorics ; Symbolic Computation Domaine(s) : Algèbre ; Combinatoires ; Informatique Format : MP4 (.mp4) - HD Durée : 01:14:19 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-03-17_Koutschan_1.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : ALEA Days / Journées ALEAOrganisateurs de la Rencontre : Fang, Wenjie ; Jugé, Vincent ; Noy, Marc ; Pivoteau, Carine Dates : 17/03/2025 - 21/03/2025 Année de la rencontre : 2025 URL de la Rencontre : https://conferences.cirm-math.fr/3341.html
Données de citation
DOI : 10.24350/CIRM.V.20327903Citer cette vidéo: Koutschan, Christoph (2025). Algorithmic methods for enumerative combinatorics - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20327903 URI : http://dx.doi.org/10.24350/CIRM.V.20327903 |
Voir Aussi
- [Multi angle] Algorithmic methods for enumerative combinatorics - lecture 2 / Auteur de la conférence Koutschan, Christoph.
- [Multi angle] Pattern avoiding 3-permutations and triangle bases / Auteur de la conférence Schabanel, Juliette.
- [Multi angle] Maths and AI / Auteur de la conférence Lelarge, Marc.
- [Multi angle] Chaînes montantes-descendantes et limites d'échelle / Auteur de la conférence Féray, Valentin.
Bibliographie
- DOUGHERTY-BLISS, Robert, KOUTSCHAN, Christoph, TER-SAAKOV, Natalya, et al. The (Symbolic and Numeric) Computational Challenges of Counting 0-1 balanced matrices. arXiv preprint arXiv:2410.07435, 2024. - https://doi.org/10.48550/arXiv.2410.07435
- KOUTSCHAN, Christoph, UNCU, Ali Kemal, et WONG, Elaine. A Unified Approach to Unimodality of Gaussian Polynomials. In : Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation. 2023. p. 434-442. - https://doi.org/10.1145/3597066.3597113
- KAUERS, Manuel et KOUTSCHAN, Christoph. Guessing with little data. In : Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation. 2022. p. 83-90. - https://doi.org/10.1145/3476446.3535486
- KOUTSCHAN, Christoph et WONG, Elaine. Exact lower bounds for monochromatic Schur triples and generalizations. In : Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra: In Honour of Peter Paule on his 60th Birthday. Cham : Springer International Publishing, 2020. p. 223-248. - https://doi.org/10.1007/978-3-030-44559-1_13
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