A Combinatorial Property of Points anf Ellipsoids
نویسندگان
چکیده
For each d-1 there is a constant Ca > 0 such that any finite set X c R a contains a subset YcX, IYI<-[~d(d+3)J +1 having the following property: if E = Y is an ellipsoid, then IE nXt-> c~JXl.
منابع مشابه
On the Minimum Volume Covering Ellipsoid of Ellipsoids
We study the problem of computing a (1+ )-approximation to the minimum volume covering ellipsoid of a given set S of the convex hull of m full-dimensional ellipsoids in Rn. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in turn, is a modification of Khachiyan’s algorithm. F...
متن کاملAsymptotic behaviour of associated primes of monomial ideals with combinatorial applications
Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. We say that $I$ satisfies the persistence property if $mathrm{Ass}_R(R/I^k)subseteq mathrm{Ass}_R(R/I^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{Ass}_R(R/I)$ denotes the set of associated prime ideals of $I$. In this paper, we introduce a class of square-free monomial ideals in the polynomial ring $R=K[x_1,ld...
متن کاملA convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
متن کاملOn the Minimum Volume Covering Ellipsoid of Ellipsoids
Let S denote the convex hull of m full-dimensional ellipsoids in Rn. Given > 0 and δ > 0, we study the problems of computing a (1 + )-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding of S. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in ...
متن کاملTopologies on Free Monoids Induced by Closure Operators of a Special Type
For S£g^>(I*) the language operator Anf# (A) is defined by {z\z\Ae<S?}. If £? fulfiiïs some properties then oc^ ( ^ ^ ^ u Anf^ (A) is a closure operator and hence topologies can be defined. These topologies are characterized by different points of view. Furthermore some topological properties are discussed in terms of properties of ££'. Resumé. — Pour unefamille.de langages j2f<=£(X*) l'opérate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete & Computational Geometry
دوره 5 شماره
صفحات -
تاریخ انتشار 1990