List questions from combinatorial-geometry

Published on 29 May 2020 - 17:25

36

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Configuration of high-dimensional spheres

Published on 31 May 2020 - 21:37

58

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Prove that,a triangle can be formed using sides equal to the diagonals of any convex pentagon.

Published on 11 Jun 2020 - 6:51

133

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An old APMO problem involving combinatorial geometry

Published on 14 Jun 2020 - 15:19

51

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For $A \in F_2^{N \times M}$ find $\mathbf x \in F_2^M$ to maximize $L_0$ norm of $A \mathbf x$

Published on 15 Jun 2020 - 10:37

157

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For $W=\cup_{U\in\mathcal U} U$ show that there exists $U_1,\dots,U_n: \ \sum_{i=1}^n \lambda(U_i) > \frac{1 - \epsilon}{3^d}\lambda(W)$

Published on 15 Jun 2020 - 12:42

49

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Trying to track down Sperner's lemma with signed counting of triangles

Published on 15 Jun 2020 - 21:19

39

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Minimal size coverings of a metric space with closed unit disks

Published on 16 Jun 2020 - 7:29

151

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Identify directly illuminated surface of a volume

Published on 17 Jun 2020 - 6:56

121

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Show that function distances are preserved

Published on 20 Jun 2020 - 1:28

890

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For $n$ points on a plane, prove that there are at most $3n$ pairs of vertices with distance 1

Published on 03 Jul 2020 - 16:22

51

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A probabilistic partisan game

Published on 15 Jul 2020 - 1:45

142

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What is the minimum embedding dimension for a given graph with unit line-segments as edges?

Published on 15 Jul 2020 - 10:11

262

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What shapes can be made with 144 tetrahedron? Or multiples 288, 432?

Published on 25 Mar 2026 - 4:40

703

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Given an $n\times n\times n$ cube, what is the largest number of $1\times 1\times 1$ blocks that a plane can cut through?

Published on 19 Jul 2020 - 8:34

List Question

A combinatorial problem in geometry (inequality)

Configuration of high-dimensional spheres

Prove that,a triangle can be formed using sides equal to the diagonals of any convex pentagon.

An old APMO problem involving combinatorial geometry

For $A \in F_2^{N \times M}$ find $\mathbf x \in F_2^M$ to maximize $L_0$ norm of $A \mathbf x$

For $W=\cup_{U\in\mathcal U} U$ show that there exists $U_1,\dots,U_n: \ \sum_{i=1}^n \lambda(U_i) > \frac{1 - \epsilon}{3^d}\lambda(W)$

Trying to track down Sperner's lemma with signed counting of triangles

Minimal size coverings of a metric space with closed unit disks

Identify directly illuminated surface of a volume

Show that function distances are preserved

For $n$ points on a plane, prove that there are at most $3n$ pairs of vertices with distance 1

A probabilistic partisan game

What is the minimum embedding dimension for a given graph with unit line-segments as edges?

What shapes can be made with 144 tetrahedron? Or multiples 288, 432?

Given an $n\times n\times n$ cube, what is the largest number of $1\times 1\times 1$ blocks that a plane can cut through?

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