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Face Posets of Tropical Polyhedra and Monomial Ideals

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Face Posets of Tropical Polyhedra and Monomial Ideals. / Loho, Georg; Smith, Ben.
In: The Electronic Journal of Combinatorics, Vol. 30, No. 4, P4.11, 20.10.2023.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Loho, G & Smith, B 2023, 'Face Posets of Tropical Polyhedra and Monomial Ideals', The Electronic Journal of Combinatorics, vol. 30, no. 4, P4.11. https://doi.org/10.37236/9999

APA

Loho, G., & Smith, B. (2023). Face Posets of Tropical Polyhedra and Monomial Ideals. The Electronic Journal of Combinatorics, 30(4), Article P4.11. https://doi.org/10.37236/9999

Vancouver

Loho G, Smith B. Face Posets of Tropical Polyhedra and Monomial Ideals. The Electronic Journal of Combinatorics. 2023 Oct 20;30(4):P4.11. doi: 10.37236/9999

Author

Loho, Georg ; Smith, Ben. / Face Posets of Tropical Polyhedra and Monomial Ideals. In: The Electronic Journal of Combinatorics. 2023 ; Vol. 30, No. 4.

Bibtex

@article{7e001120431945739358e1f9aa36ab91,
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",
year = "2023",
month = oct,
day = "20",
doi = "10.37236/9999",
language = "English",
volume = "30",
journal = "The Electronic Journal of Combinatorics",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "4",

}

RIS

TY - JOUR

T1 - Face Posets of Tropical Polyhedra and Monomial Ideals

AU - Loho, Georg

AU - Smith, Ben

PY - 2023/10/20

Y1 - 2023/10/20

N2 - 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.

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.

UR - https://research.manchester.ac.uk/en/publications/d0fdfd3a-bd15-412e-88b1-b80773c9f38d

U2 - 10.37236/9999

DO - 10.37236/9999

M3 - Journal article

VL - 30

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 4

M1 - P4.11

ER -