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Algorithmic methods for enumerative combinatorics - lecture 1
Multi angle
Authors : Koutschan, Christoph (Author of the conference)
CIRM (Publisher )
05A19 - Combinatorial identities, bijective combinatorics
05A20 - Combinatorial inequalities
68W30 - Symbolic computation and algebraic computation
47L20 - Operator ideals
Additional resources :
https://www.cirm-math.fr/RepOrga/3341/Slides/cours-koutschan-final.pdf
CIRM (Publisher )
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Abstract :
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.
Keywords : cylindrical algebraic decomposition; CAD; lattice reduction; LLL; recurrence guessing; D-finite function; creative telescoping
MSC Codes : Keywords : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/3341/Slides/cours-koutschan-final.pdf
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 00/00/0000 Conference Date : 17/03/2025 Subseries : Research School arXiv category : Combinatorics ; Symbolic Computation Mathematical Area(s) : Algebra ; Combinatorics ; Computer Science Format : MP4 (.mp4) - HD Video Time : 01:14:19 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-03-17_Koutschan_1.mp4 
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Information on the Event
Event Title : ALEA Days / Journées ALEAEvent Organizers : Fang, Wenjie ; Jugé, Vincent ; Noy, Marc ; Pivoteau, Carine Dates : 17/03/2025 - 21/03/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3341.html
Citation Data
DOI : 10.24350/CIRM.V.20327903Cite this video as: 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 |
See Also
- [Multi angle] Algorithmic methods for enumerative combinatorics - lecture 2 / Author of the conference Koutschan, Christoph.
- [Multi angle] Pattern avoiding 3-permutations and triangle bases / Author of the conference Schabanel, Juliette.
- [Multi angle] Maths and AI / Author of the conference Lelarge, Marc.
- [Multi angle] Chaînes montantes-descendantes et limites d'échelle / Author of the conference Féray, Valentin.
Bibliography
- 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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