Geodesic
The \(\nu \)-Tamari lattice via \(\nu \)-trees, \( \nu \)-bracket vectors, and subword complexes
Cesar Ceballos1 ; Arnau Padrol2 ; Camilo Sarmiento3
1Faculty of Mathematics, University of Vienna
2Sorbonne Université, Institut de Mathématiques de Jussieu - Paris Rive Gauche (UMR 7586)
3Departamento de Matemáticas y Estadística, Universidad del Norte
The electronic journal of combinatorics, Tome 27 (2020) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We give a new interpretation of the $\nu$-Tamari lattice of Préville-Ratelle and Viennot in terms of a rotation lattice of $\nu$-trees. This uncovers the relation with known combinatorial objects such as north-east fillings, \mbox{tree-like} tableaux and subword complexes. We provide a simple description of the lattice property using certain bracket vectors of $\nu$-trees, and show that the Hasse diagram of the $\nu$-Tamari lattice can be obtained as the facet adjacency graph of certain subword complex. Finally, this point of view generalizes to multi $\nu$-Tamari complexes, and gives (conjectural) insight on their geometric realizability via polytopal subdivisions of multiassociahedra.
DOI : 10.37236/8000
Classification : 06A07, 05E45, 05E10, 05A05, 05A19

Cesar Ceballos  1   ; Arnau Padrol  2   ; Camilo Sarmiento  3

1 Faculty of Mathematics, University of Vienna
2 Sorbonne Université, Institut de Mathématiques de Jussieu - Paris Rive Gauche (UMR 7586)
3 Departamento de Matemáticas y Estadística, Universidad del Norte 
@article{10_37236_8000,
     author = {Cesar Ceballos and Arnau Padrol and Camilo Sarmiento},
     title = {The \(\nu {\)-Tamari} lattice via \(\nu \)-trees, \( \nu \)-bracket vectors, and subword complexes},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {1},
     doi = {10.37236/8000},
     zbl = {1480.06003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8000/}
}
TY  - JOUR
AU  - Cesar Ceballos
AU  - Arnau Padrol
AU  - Camilo Sarmiento
TI  - The \(\nu \)-Tamari lattice via \(\nu \)-trees, \( \nu \)-bracket vectors, and subword complexes
JO  - The electronic journal of combinatorics
PY  - 2020
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/8000/
DO  - 10.37236/8000
ID  - 10_37236_8000
ER  - 
%0 Journal Article
%A Cesar Ceballos
%A Arnau Padrol
%A Camilo Sarmiento
%T The \(\nu \)-Tamari lattice via \(\nu \)-trees, \( \nu \)-bracket vectors, and subword complexes
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8000/
%R 10.37236/8000
%F 10_37236_8000
Cesar Ceballos; Arnau Padrol; Camilo Sarmiento. The \(\nu \)-Tamari lattice via \(\nu \)-trees, \( \nu \)-bracket vectors, and subword complexes. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8000

Cité par Sources :