Geodesic
A consecutive Lehmer code for parabolic quotients of the symmetric group
Wenjie Fang ; Henri Mühle1 ; Jean-Christophe Novelli
1TU Dresden Institut für Algebra
The electronic journal of combinatorics, Tome 28 (2021) no. 3

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl DOI arXiv
In this article we define an encoding for parabolic permutations that distinguishes between parabolic $231$-avoiding permutations. We prove that the componentwise order on these codes realizes the parabolic Tamari lattice, and conclude a direct and simple proof that the parabolic Tamari lattice is isomorphic to a certain $\nu$-Tamari lattice, with an explicit bijection. Furthermore, we prove that this bijection is closely related to the map $\Theta$ used when the lattice isomorphism was first proved in (Ceballos, Fang and Mühle, 2020), settling an open problem therein.
DOI : 10.37236/10578
Classification : 05A19, 06B99
Mots-clés : symmetric group, Tamari lattice, parabolic quotient, Lehmer code

Wenjie Fang    ; Henri Mühle  1   ; Jean-Christophe Novelli 

1 TU Dresden Institut für Algebra 
Wenjie Fang; Henri Mühle; Jean-Christophe Novelli. A consecutive Lehmer code for parabolic quotients of the symmetric group. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10578
@article{10_37236_10578,
     author = {Wenjie Fang and Henri M\"uhle and Jean-Christophe Novelli},
     title = {A consecutive {Lehmer} code for parabolic quotients of the symmetric group},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/10578},
     zbl = {1483.05012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10578/}
}
TY  - JOUR
AU  - Wenjie Fang
AU  - Henri Mühle
AU  - Jean-Christophe Novelli
TI  - A consecutive Lehmer code for parabolic quotients of the symmetric group
JO  - The electronic journal of combinatorics
PY  - 2021
VL  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/10578/
DO  - 10.37236/10578
ID  - 10_37236_10578
ER  - 
%0 Journal Article
%A Wenjie Fang
%A Henri Mühle
%A Jean-Christophe Novelli
%T A consecutive Lehmer code for parabolic quotients of the symmetric group
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10578/
%R 10.37236/10578
%F 10_37236_10578

Cité par Sources :