A well known theorem of Tverberg states that if n ≥ T ( d , r ), then one can partition any set of n points in R d into r pairwise disjoint subsets whose convex hulls have a common point. The numbers T ( d , r ) are known as Tverberg numbers. Reay added another parameter k...
Tverberg's theorem says that a set with sufficiently many points in Rd can always be partitioned into m parts so that the (m-1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. The main results of our paper demonstrate that Tverberg's theorem is just a ...
We present projective versions of the center point theorem and Tverberg’s theorem, interpolating between the original and the so-called “dual” center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful...
Tverberg’s theorem states that a set with sufficiently many points in $${\mathbb {R}}^d$$ can always be partitioned into m parts such that the nerve
A theorem of Tverberg from 1966 asserts that every set X d of n = T ( d , r ) = ( d + 1)( r 1) + 1 points can be partitioned into r pairwise disjoint subsets, whose convex hulls have a point in common. Thus every such partition induces an integer partition of n into r ...
For example, we provide a linear time algorithm for computing a "fuzzy" centerpoint, and prove a no-dimensional weak ε \\varepsilon -net theorem with an improved constant.Springer USDiscrete & Computational GeometryHar-Peled, SarielDepartment of Computer Science, University of Illinois, Urbana-...
Tverberg, A proof of the Jordan curve theorem, Bull. London Math. Soc... T Helge - 《Bulletin of the London Mathematical Society》 被引量: 37发表: 1980年 Enumeration of the degree sequences of non-separable graphs and connected graphs In 1962, S. L. Hakimi proved necessary and sufficient...
Reay, J. R. (1979) Several Generalizations of Tverberg's Theorem. Israël J. Math. 34: pp. 238-244J.R. Reay, (1978) Several generalizations of Tverberg’s theorem. Israel J. Math. To appear. (See also: Radon type theorems without independence conditions. Notices Amer. Math. Soc. ...
Crossing Tverberg theoremThe Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r-1)+1 points in R^d, one can find a partition X=X_1 cup ... cup X_r of X, such that the convex hulls of the X_i, i=1,......
Helly's theoremLatticesTverberg's theorem2017 Springer Science+Business Media New YorkThis paper presents a new variation of Tverberg's theorem. Given a discrete set S of (Formula presented.), we study the number of points of S needed to guarantee the existence of an m-partition of the ...