منابع مشابه
Notes on lattice points of zonotopes and lattice-face polytopes
Minkowski’s second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski’s bound by replacing the volume by the lattice point enumerator of a convex body. To this we are interested in bounds on the coefficients of Ehrhart polynomials of lattice polytopes via the successive minima. Our resu...
متن کاملInterpolation, box splines, and lattice points in zonotopes
Given a finite list of vectors X ⊆ R, one can define the box spline BX . Box splines are piecewise polynomial functions that are used in approximation theory. They are also interesting from a combinatorial point of view and many of their properties solely depend on the structure of the matroid defined by the list X . The support of the box spline is the zonotope Z(X). We show that if the list X...
متن کاملOn the diameter of lattice polytopes
In this paper we show that the diameter of a d-dimensional lattice polytope in [0, k]n is at most
متن کاملPrimitive Zonotopes
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.
متن کاملDiameter series of lattice covering simplices
We develop an interesting relationship between /nite sets in a lattice and the minimal density of simplex coverings of n-space. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2020
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14977