Face Posets of Tropical Polyhedra and Monomial Ideals

Georg Loho, Ben Smith

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
JournalThe Electronic Journal of Combinatorics
Issue number4
Publication statusPublished - 20 Oct 2023


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