Lattice congruences for combinatorialists | Vidéo | Carmin.tv

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Lattice congruences for combinatorialists

By Nathan Reading

Appears in 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.

Information about the video

Date of recording 01/12/2025
Date of publication 17/12/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20413403
Cite this video 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

Domain(s)

Combinatorics

Bibliography

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

MSC codes

Document(s)

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

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