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Results tagged with discrete-geometry
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user 468
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
5
votes
Accepted
Functionals on oriented matroids
I think the answer to your first question is "yes".
Oriented matroids can be realized topologically, and I am going to use that language. (This means is that I can pretend the oriented matroid is …
- 6,327
5
votes
Accepted
Counting lattice points inside a parallelepiped
I have not filled in absolutely all the details, but hopefully this is enough to be convincing.
Let's let $M$ take positive integer values, and let's consider the parallelepiped: $$P'=\{x+Mtv\mid x\in …
- 6,327
2
votes
What's the difference between a PL simplicial sphere and a shellable simplicial sphere?
I think the question is slightly missing the point, in a way that it may be useful to explain. Frequently, the reason you would want to show something is a shellable simplicial sphere is in order to b …
- 6,327
0
votes
Accepted
number of affine pieces of linear interpolation of convex functions in high dimension
Let's think of choosing the values of $f$ at the grid points one grid point at a time, in such a way that the result is convex.
If you work systematically through the grid points in an order so t …
- 6,327