Face Posets of Tropical Polyhedra and Monomial Ideals

Loho, Georg and Smith, Ben (2023) Face Posets of Tropical Polyhedra and Monomial Ideals. The Electronic Journal of Combinatorics, 30 (4): P4.11. ISSN 1077-8926

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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.

Item Type:

Journal Article

Journal or Publication Title:

The Electronic Journal of Combinatorics

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/1700/1703

Subjects:

?? computational theory and mathematicsgeometry and topologytheoretical computer science ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

225360

Deposited By:

ep_importer_pure

Deposited On:

30 Oct 2024 14:30

Refereed?:

Yes

Published?:

Published

Last Modified:

06 Nov 2024 19:10

URI:

https://eprints.lancs.ac.uk/id/eprint/225360