The extra slow Tamari lattice
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918513694736384 |
|---|---|
| author | Corteel, Sylvie Jang, Jihyeug Rognerud, Baptiste |
| author_facet | Corteel, Sylvie Jang, Jihyeug Rognerud, Baptiste |
| contents | We introduce the extra slow Tamari lattices, a new family of lattices defined on faithfully balanced tableaux. These tableaux arise naturally from the representation theory of type \( A \) quivers, and our construction extends the classical Tamari lattice and the slow Tamari lattice.
We explicitly describe meets and joins in the extra slow Tamari lattices, and then prove that they are lattices. We then show that they are semidistributive, trim, polygonal, and congruence uniform. Their join-irreducible elements are described in terms of a three-color analogue of the positive roots of type \( A \), which leads to descriptions of their spines and congruence lattices. We also obtain several enumerative results for the extra slow Tamari lattices and their associated structures. Finally, we derive new structural and enumerative results for the slow Tamari lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20903 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The extra slow Tamari lattice Corteel, Sylvie Jang, Jihyeug Rognerud, Baptiste Combinatorics 05A15, 06A07, 06B10 We introduce the extra slow Tamari lattices, a new family of lattices defined on faithfully balanced tableaux. These tableaux arise naturally from the representation theory of type \( A \) quivers, and our construction extends the classical Tamari lattice and the slow Tamari lattice. We explicitly describe meets and joins in the extra slow Tamari lattices, and then prove that they are lattices. We then show that they are semidistributive, trim, polygonal, and congruence uniform. Their join-irreducible elements are described in terms of a three-color analogue of the positive roots of type \( A \), which leads to descriptions of their spines and congruence lattices. We also obtain several enumerative results for the extra slow Tamari lattices and their associated structures. Finally, we derive new structural and enumerative results for the slow Tamari lattices. |
| title | The extra slow Tamari lattice |
| topic | Combinatorics 05A15, 06A07, 06B10 |
| url | https://arxiv.org/abs/2605.20903 |