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Mating of discrete trees and walks in the quarter plane
Multi angle
Authors : Biane, Philippe (Author of the conference)
CIRM (Publisher )
05A19 - Combinatorial identities, bijective combinatorics
05C05 - Trees
05C38 - Paths and cycles
CIRM (Publisher )
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Abstract :
We give a general construction of triangulations, starting from a walk with small steps in the quarter plane This construction is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps equipped with a rooted spanning tree and walks in the quarter plane. We also show how the construction allows to recover several known bijections between such objects in a uniform way.
Keywords : arbre; chemin; carte
MSC Codes : Keywords : arbre; chemin; carte
05A19 - Combinatorial identities, bijective combinatorics
05C05 - Trees
05C38 - Paths and cycles
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/08/2021 Conference Date : 24/06/2021 Subseries : Research talks arXiv category : Combinatorics Mathematical Area(s) : Combinatorics Format : MP4 (.mp4) - HD Video Time : 01:04:12 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-06-24_Biane.mp4 
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Information on the Event
Event Title : Lattice Paths, Combinatorics and Interactions / Marches aléatoires, combinatoire et interactionsEvent Organizers : Banderier, Cyril ; Dousse, Jehanne ; Duchi, Enrica ; Krattenthaler, Christian ; Wallner, Michael Dates : 21/06/2021 - 25/06/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2324.html
Citation Data
DOI : 10.24350/CIRM.V.19770203Cite this video as: Biane, Philippe (2021). Mating of discrete trees and walks in the quarter plane. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19770203 URI : http://dx.doi.org/10.24350/CIRM.V.19770203 |
See Also
- [Virtualconference] Using symbolic dynamical programming in lattice paths combinatorics / Author of the conference Zeilberger, Doron.
- [Virtualconference] The alternating sign matrices and descending plane partitions : n+3 pairs of equivalent statistics / Author of the conference Fischer, Ilse.
- [Multi angle] Lattice paths and heaps / Author of the conference Viennot, Xavier.
- [Virtualconference] Bijections between walks inside a triangular domain and Motzkin paths of bounded amplitude / Author of the conference Marcovici, Irène.
- [Virtualconference] Random triangulations and bijective paths to Liouville quantum gravity / Author of the conference Holden, Nina.
Bibliography
- BIANE, Philippe. Mating of discrete trees and walks in the quarter-plane. arXiv preprint arXiv:2101.12590, 2021. - https://arxiv.org/abs/2101.12590
