k-Sets and k-Facets

نویسندگان

  • Uli Wagner
  • ULI WAGNER
چکیده

We survey problems, results, and methods concerning k-facets and k-sets of finite point sets in real affine d-space and the dual notion of levels in arrangements of hyperplanes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

New methods for constructing shellable simplicial complexes

A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...

متن کامل

Number of Minimal Path Sets in a Consecutive-k-out-of-n: F System

In this paper the combinatorial problem of determining the number of minimal path sets of a consecutive-k-out-of-n: F system is considered. For the cases where k = 2, 3 the explicit formulae are given and for k ≥ 4 a recursive relation is obtained. Direct computation for determining the number of minimal path sets of a consecutive-k-out-of-n: F system for k ≥ 4 remains a difficult task. ...

متن کامل

K-sets and J-facets -a Tour of Discrete Geometry a Very Preliminary Version

This paper gives an account of the most important facts about k-sets, j-facets and k-levels. First, we describe the fundamental properties of the objects under discussion and some related ones. We also show connections between them. In the next part, we list the historical as well as the currently best bounds on the number of k-sets (or, equivalently, bounds on the complexity of k-levels). Then...

متن کامل

k-TUPLE DOMATIC IN GRAPHS

For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination...

متن کامل

k-sets and continuous motion in R3

We prove several new results concerning k-sets of point sets on the 2-sphere (equivalently, for signed point sets in the plane) and k-sets in 3-space. Specific results include spherical generalizations of (i) Lovász’ lemma (regarding the number of spherical k-edges intersecting a given great circle) and of (ii) the crossing identity for kedges due to Andrzejak et al. As a new ingredient compare...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007