Face Posets of Tropical Polyhedra and Monomial Ideals

Georg Loho; Ben Smith

doi:10.37236/9999

Face Posets of Tropical Polyhedra and Monomial Ideals

Georg Loho, Ben Smith

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	The Electronic Journal of Combinatorics
Volume	30
Issue number	4
DOIs	https://doi.org/10.37236/9999
Publication status	Published - 20 Oct 2023

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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.",

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AB - 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.

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DO - 10.37236/9999

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JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

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Face Posets of Tropical Polyhedra and Monomial Ideals

Abstract

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