We study parabolic aligned elements associated with the type-$B$ Coxeter group and the so-called linear Coxeter element. These elements were introduced algebraically in (Mühle and Williams, 2019) for parabolic quotients of finite Coxeter groups and were characterized by a certain forcing condition on inversions. We focus on the type-$B$ case and give a combinatorial model for these elements in terms of pattern avoidance. Moreover, we describe an equivalence relation on parabolic quotients of the type-$B$ Coxeter group whose equivalence classes are indexed by the aligned elements. We prove that this equivalence relation extends to a congruence relation for the weak order. The resulting quotient lattice is the type-$B$ analogue of the parabolic Tamari lattice introduced for type $A$ in (Mühle and Williams, 2019).
@article{10_37236_12157,
author = {Wenjie Fang and Henri M\"uhle and Jean-Christophe Novelli},
title = {Parabolic {Tamari} lattices in linear type {\(B\)}},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {1},
doi = {10.37236/12157},
zbl = {7834200},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12157/}
}
TY - JOUR
AU - Wenjie Fang
AU - Henri Mühle
AU - Jean-Christophe Novelli
TI - Parabolic Tamari lattices in linear type \(B\)
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/12157/
DO - 10.37236/12157
ID - 10_37236_12157
ER -
%0 Journal Article
%A Wenjie Fang
%A Henri Mühle
%A Jean-Christophe Novelli
%T Parabolic Tamari lattices in linear type \(B\)
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/12157/
%R 10.37236/12157
%F 10_37236_12157
Wenjie Fang; Henri Mühle; Jean-Christophe Novelli. Parabolic Tamari lattices in linear type \(B\). The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12157
