Sortable elements and Cambrian lattices
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2005
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916005592170496 |
|---|---|
| author | Reading, Nathan |
| author_facet | Reading, Nathan |
| contents | We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0512339 |
| institution | arXiv |
| publishDate | 2005 |
| record_format | arxiv |
| spellingShingle | Sortable elements and Cambrian lattices Reading, Nathan Combinatorics 20F55, 06B10 We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W. |
| title | Sortable elements and Cambrian lattices |
| topic | Combinatorics 20F55, 06B10 |
| url | https://arxiv.org/abs/math/0512339 |