For any finite, connected poset $P$, we show that the $f$-vector of Galashin's $P$-associahedron $\mathscr A(P)$ only depends on the comparability graph of $P$. In particular, this allows us to produce a family of polytopes with the same $f$-vectors as permutohedra, but that are not combinatorially equivalent to permutohedra.
@article{10_37236_13422,
author = {Son Nguyen and Andrew Sack},
title = {The {\(P\)-associahedron} \(f\)-vector is a comparability invariant},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {4},
doi = {10.37236/13422},
zbl = {8120097},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13422/}
}
TY - JOUR
AU - Son Nguyen
AU - Andrew Sack
TI - The \(P\)-associahedron \(f\)-vector is a comparability invariant
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/13422/
DO - 10.37236/13422
ID - 10_37236_13422
ER -
%0 Journal Article
%A Son Nguyen
%A Andrew Sack
%T The \(P\)-associahedron \(f\)-vector is a comparability invariant
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/13422/
%R 10.37236/13422
%F 10_37236_13422
Son Nguyen; Andrew Sack. The \(P\)-associahedron \(f\)-vector is a comparability invariant. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13422
