The associahedron is classically constructed as a removahedron, i.e. by deleting inequalities in the facet description of the permutahedron. This removahedral construction extends to all permutreehedra (which interpolate between the permutahedron, the associahedron and the cube). Here, we investigate removahedra constructions for all quotientopes (which realize the lattice quotients of the weak order). On the one hand, we observe that the permutree fans are the only quotient fans realized by a removahedron. On the other hand, we show that any permutree fan can be realized by a removahedron constructed from any realization of the braid fan. Our results finally lead to a complete description of the type cones of the permutree fans.
@article{10_37236_10214,
author = {Doriann Albertin and Vincent Pilaud and Julian Ritter},
title = {Removahedral congruences versus permutree congruences},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {4},
doi = {10.37236/10214},
zbl = {1475.52017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10214/}
}
TY - JOUR
AU - Doriann Albertin
AU - Vincent Pilaud
AU - Julian Ritter
TI - Removahedral congruences versus permutree congruences
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10214/
DO - 10.37236/10214
ID - 10_37236_10214
ER -
%0 Journal Article
%A Doriann Albertin
%A Vincent Pilaud
%A Julian Ritter
%T Removahedral congruences versus permutree congruences
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10214/
%R 10.37236/10214
%F 10_37236_10214
Doriann Albertin; Vincent Pilaud; Julian Ritter. Removahedral congruences versus permutree congruences. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10214
