Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer_journal/primitive-zonotopes-RM8jftzWLf
References (19)
-
F Santos (2012)
A counterexample to the Hirsch conjectureAnn. Math., 176
-
B Grünbaum (2003)
Convex Polytopes. Graduate Texts in Mathematics -
DM Acketa, JD Žunić (1995)
On the maximal number of edges of convex digital polygons included into an $$m\times {m}$$ m × m -gridJ. Comb. Theory Ser. A, 69
-
M Melamed, S Onn (2014)
Convex integer optimization by constantly many linear counterpartsLinear Algebra Appl., 447
-
S Onn (2010)
Nonlinear Discrete Optimization. Zurich Lectures in Advanced Mathematics. -
D Naddef (1989)
The Hirsch conjecture is true for $$(0,1)$$ ( 0 , 1 ) -polytopesMath. Program., 45
-
N Bonifas, M Summa, F Eisenbrand, N Hähnle, M Niemeier (2014)
On sub-determinants and the diameter of polyhedraDiscrete Comput. Geom., 52
-
P Gritzmann, B Sturmfels (1993)
Minkowski addition of polytopes: complexity and applications to Gröbner basesSIAM J. Discrete Math., 6
-
GH Hardy, EM Wright (1979)
An Introduction to the Theory of Numbers -
MJ Todd (2014)
An improved Kalai-Kleitman bound for the diameter of a polyhedronSIAM J. Discrete Math., 28
-
D Eppstein (1996)
Zonohedra and zonotopesMath. Educ. Res., 5
-
I Soprunov, J Soprunova (2016)
Eventual quasi-linearity of the Minkowski lengthEur. J. Comb., 58
-
P Kleinschmidt, S Onn (1992)
On the diameter of convex polytopesDiscrete Math., 102
-
G Kalai, DJ Kleitman (1992)
A quasi-polynomial bound for the diameter of graphs of polyhedraBull. Am. Math. Soc., 26
-
C Berge (1983)
Graphes -
JE Humphreys (1990)
Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics -
A Pia, C Michini (2016)
On the diameter of lattice polytopesDiscrete Comput. Geom., 55
-
GM Ziegler (1995)
Lectures on Polytopes. Graduate Texts in Mathematics -
S Onn, UG Rothblum (2004)
Convex combinatorial optimizationDiscrete Comput. Geom., 32
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer Science+Business Media New York
- Subject
- Mathematics; Combinatorics; Computational Mathematics and Numerical Analysis
- ISSN
- 0179-5376
- eISSN
- 1432-0444
- DOI
- 10.1007/s00454-017-9873-z
- Publisher site
- See Article on Publisher Site
Abstract
We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type $$B_d$$ 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.
Journal
Discrete & Computational Geometry – Springer Journals
Published: Feb 28, 2017