We exhibit several posets arising from commutative algebra, order theory, tropical convexity as potential face posets of tropical polyhedra, and we clarify their inclusion relations. We focus on monomial tropical polyhedra, and deduce how their geometry reflects properties of monomial ideals. Their vertex-facet lattice is homotopy equivalent to a sphere and encodes the Betti numbers of an associated monomial ideal.
@article{10_37236_9999,
author = {Georg Loho and Ben Smith},
title = {Face posets of tropical polyhedra and monomial ideals},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/9999},
zbl = {1550.14058},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9999/}
}
TY - JOUR
AU - Georg Loho
AU - Ben Smith
TI - Face posets of tropical polyhedra and monomial ideals
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/9999/
DO - 10.37236/9999
ID - 10_37236_9999
ER -
%0 Journal Article
%A Georg Loho
%A Ben Smith
%T Face posets of tropical polyhedra and monomial ideals
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9999/
%R 10.37236/9999
%F 10_37236_9999
Georg Loho; Ben Smith. Face posets of tropical polyhedra and monomial ideals. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/9999
