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Tverberg's theorem

Index Tverberg's theorem

In discrete geometry, Tverberg's theorem, first stated by, is the result that sufficiently many points in d-dimensional Euclidean space can be partitioned into subsets with intersecting convex hulls. [1]

9 relations: Convex hull, Discrete geometry, Euclidean space, Heptagon, London Mathematical Society, Partition of a set, Radon's theorem, Rota's basis conjecture, Subset.

Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

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Discrete geometry

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Heptagon

In geometry, a heptagon is a seven-sided polygon or 7-gon.

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London Mathematical Society

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).

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Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

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Radon's theorem

In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of d + 2 points in Rd can be partitioned into two disjoint sets whose convex hulls intersect.

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Rota's basis conjecture

In linear algebra and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named after Gian-Carlo Rota.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Redirects here:

Tverberg partition, Tverberg partition theorem, Tverberg theorem, Tverberg's partition theorem.

References

[1] https://en.wikipedia.org/wiki/Tverberg's_theorem

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