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Results tagged with convex-polytopes
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user 11674
Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming
5
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2
answers
642
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Is there a simple test to determine whether a polytope is integral?
It is known that any rational convex polytope expressed as $\{ x\in\mathbb{R}^d : Ax \ge b \}$, where $A\in\mathbb{Z}^{k\times d}$ and $b\in\mathbb{Z}^k$, can be written as the convex hull of finitely …
- 170
3
votes
Accepted
Classification of lattice polytopes with small number of lattice points in the facets
This is something you might be aware of already (and which does not seem to be exactly the situation you are formulating), but Reeve's tetrahedron is a 3-dimensional integral convex polytope without l …
- 170
1
vote
0
answers
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Lattice-point enumeration question involving linear combinations of matrices
I would like to know some references to learn more about an answer to this question, if there are any references:
Let $A_1, \dots , A_m$ and $B$ be $n\times n$ symmetric matrices. Let $$S = \{(x_1, …
- 170