The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions.Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph,...
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 ...
In a generalization of Radon's theorem, Tverberg showed that each set S of at least ( d +1) ( r − 1)+1 points in R d has an r -partition into (pair wise disjoint) subsets S = S 1 ∪…∪ S r so that \\\(\\\bigcapolimits_i^r {\\\underline{\\\underline {}} } _...
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 Rd can always be partitioned into m parts such that the nerve (the intersection pattern) of the convex hulls of the parts form an (m−1)-simplex. De Loera, Hogan, Oliveros, and Yang (2021) explored how other simpl...
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...
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 states that for any k ≥ 2 and any set P Rd of at least (d + 1)(k - 1) + 1 points in d dimensions, we can partition P into k subsets whose convex hulls have a non-empty intersection. The associated search problem of find- ing the partition lies in the ...
The topological Tverberg theorem states that any continuous map of a (d+1)(r1)$(d+1)(r-1)$‐simplex into the Euclidean d$d$‐space maps some points from r$r$ pairwise disjoint faces of the simplex to the same point whenever r$r$ is a prime power. We substantially generalize this ...
Tverberg's theorem is a result from discrete geometry, which states that, in any d-dimensional vector space for any set of (k-1 ){d + 1) + 1 points in that vector space, the set can be partitioned into k disjoint subsets, the convex hulls of which are intersecting. The paper at ...