Details
| Original language | English |
|---|---|
| Pages (from-to) | 611-639 |
| Number of pages | 29 |
| Journal | SIAM Journal on Discrete Mathematics |
| Volume | 34 |
| Issue number | 1 |
| Publication status | Published - 3 Mar 2020 |
Abstract
For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial type of the polytopes is constant when the parameters vary in the relative interior of each face of the hypercube. Moreover, with the help of a subdivision arising from a tropical hyperplane arrangement associated to the marked poset, we give an explicit description of the vertices of the polytope for generic parameters.
Keywords
- Lattice polytopes, Marked poset polytopes, Tropical geometry
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: SIAM Journal on Discrete Mathematics, Vol. 34, No. 1, 03.03.2020, p. 611-639.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Continuous Family of Marked Poset Polytopes
AU - Fang, Xin
AU - Fourier, Ghislain
AU - Litza, Jan-philipp
AU - Pegel, Christoph
PY - 2020/3/3
Y1 - 2020/3/3
N2 - For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial type of the polytopes is constant when the parameters vary in the relative interior of each face of the hypercube. Moreover, with the help of a subdivision arising from a tropical hyperplane arrangement associated to the marked poset, we give an explicit description of the vertices of the polytope for generic parameters.
AB - For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial type of the polytopes is constant when the parameters vary in the relative interior of each face of the hypercube. Moreover, with the help of a subdivision arising from a tropical hyperplane arrangement associated to the marked poset, we give an explicit description of the vertices of the polytope for generic parameters.
KW - Lattice polytopes
KW - Marked poset polytopes
KW - Tropical geometry
UR - http://www.scopus.com/inward/record.url?scp=85091327982&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1712.01037
DO - 10.48550/arXiv.1712.01037
M3 - Article
VL - 34
SP - 611
EP - 639
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
SN - 0895-4801
IS - 1
ER -