@article{abb306ec3fe44641a16ef4899bd420dc,
title = "Face Posets of Tropical Polyhedra and Monomial Ideals",
abstract = "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.",
author = "Georg Loho and Ben Smith",
note = "Funding Information: The first author was supported by the ERC Starting Grant ScaleOpt and by the Swiss National Science Foundation (SNSF) within the project Convexity, geometry of numbers, and the complexity of integer programming (Nr. 163071). The second author was supported by the EPSRC grant Arrangements of tropical linear spaces (1673882) and the Heilbronn Institute for Mathematical Research. Publisher Copyright: {\textcopyright} The authors. Released under the CC BY-ND license (International 4.0).",
year = "2023",
month = oct,
day = "20",
doi = "10.37236/9999",
language = "English",
volume = "30",
journal = "Electronic Journal of Combinatorics",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "4",
}