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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

13 votes
Accepted

Is a given point in the interior of the convex hull of a given finite collection of points?

Take your linear program and add the objective function max $x$, and the inequalities $\lambda_i - x \geq 0$. If the point is on the exterior, the optimum solution has $x=0$. Otherwise, there is a sol …
Peter Shor's user avatar
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6 votes
Accepted

Expected Degree of a vertex in Delaunay Triangulations

The expected degree for the Delaunay triangulation on hyperbolic space will depend on the density of the points. With low enough density points, you should get arbitrarily high degree. You should be a …
Peter Shor's user avatar
  • 6,342
4 votes

Large subgroups of the Hamming cube

You can get half of the elements small. Let $e_k$ be the element $(0,0,\ldots,0,1,0, \ldots 0)$ with a single $1$ in the $k$th position. Let $v$ be the element $(1,1,1,1,1,\ldots,1)$. Now, consider th …
Peter Shor's user avatar
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5 votes

Forbidden mirror sequences

Here is a possible way of producing such forbidden configurations. Suppose you have $(ab)^k$ for some large $k$. Then I'd like to claim that $a$ and $b$ must be nearly parallel (see Thurston's answer) …
Peter Shor's user avatar
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10 votes
Accepted

How many non-equivalent sections of a regular 7-simplex?

Here's the answer. The main claims (Claims 1-4) I am fairly sure I got right, but I could easily have missed a case (or counted an extra case) in the later enumeration. If anybody finds a mistake, ple …
Peter Shor's user avatar
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