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Lattice congruences for combinatorialists

De Nathan Reading

Apparaît dans la collection : Beyond Permutahedra and Associahedra / Au-dela du Permutoèdre et de l'associaèdre

We will begin with the basic facts about congruences on finite lattices that every combinatorialist should see, emphasizing the ideas most relevant to the weak order on a finite Coxeter group (and also to the framing lattices that will appear in Martha Yip's lectures). We apply these facts to the weak order, motivated by examples, and develop the combinatorics of congruences/quotients, in general and in specific. If time allows, we will place the lattice theory in the geometric setting of hyperplane arrangements, posets of regions, and shards.

Informations sur la vidéo

Date de captation 01/12/2025
Date de publication 17/12/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20413403
Citer cette vidéo Reading, Nathan (01/12/2025). Lattice congruences for combinatorialists. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20413403
URL https://dx.doi.org/10.24350/CIRM.V.20413403

Domaine(s)

Combinatoire

Bibliographie

READING, Nathan. Cambrian lattices. Advances in Mathematics, 2006, vol. 205, no 2, p. 313-353. - https://doi.org/10.1016/j.aim.2005.07.010
READING, Nathan. From the Tamari lattice to Cambrian lattices and beyond. In : Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift. Basel : Springer Basel, 2012. p. 293-322. - https://doi.org/10.1007/978-3-0348-0405-9_15
READING, Nathan. Noncrossing arc diagrams and canonical join representations. SIAM Journal on Discrete Mathematics, 2015, vol. 29, no 2, p. 736-750. - https://doi.org/10.1137/140972391
READING, Nathan. Lattice theory of the poset of regions. In : Lattice Theory: Special Topics and Applications: Volume 2. Cham : Springer International Publishing, 2016. p. 399-487. - https://doi.org/10.1007/978-3-319-44236-5_9
READING, Nathan. Finite Coxeter groups and the weak order. In : Lattice Theory: Special Topics and Applications: Volume 2. Cham : Springer International Publishing, 2016. p. 489-561. - https://doi.org/10.1007/978-3-319-44236-5_10

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/3288/Slides/CIRM1.pdf

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