Primitive Zonotopes

Antoine Deza; George Manoussakis; Shmuel Onn

doi:10.1007/s00454-017-9873-z

Primitive Zonotopes

Antoine Deza, George Manoussakis, Shmuel Onn

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

17 Scopus citations

Abstract

We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type B_d. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k, and with the computational complexity of multicriteria matroid optimization.

Original language	English
Pages (from-to)	27-39
Number of pages	13
Journal	Discrete and Computational Geometry
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/s00454-017-9873-z
State	Published - 1 Jul 2018
Externally published	Yes

Keywords

Diameter
Lattice polytopes
Matroid optimization
Primitive integer vectors

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-017-9873-z

Cite this

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title = "Primitive Zonotopes",

abstract = "We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type Bd. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k, and with the computational complexity of multicriteria matroid optimization.",

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author = "Antoine Deza and George Manoussakis and Shmuel Onn",

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AU - Manoussakis, George

AU - Onn, Shmuel

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AB - We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type Bd. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k, and with the computational complexity of multicriteria matroid optimization.

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KW - Lattice polytopes

KW - Matroid optimization

KW - Primitive integer vectors

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Primitive Zonotopes

Abstract

Keywords

ASJC Scopus subject areas

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