Timeline for Lattice points in dilated polytopes and sumsets
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2014 at 19:31 | comment | added | Per Alexandersson | I had that feeling: Only a couple of years ago, a proof was provided that some GT-polytopes have non-integral vertices, and there is no known characterization on which polytopes are integral. Hence, finding the vertices (in general), is hard. For a specific instance, one can do it, but it requires a lot of work. | |
| Feb 20, 2014 at 12:23 | comment | added | Lev Borisov | If you can't even find the points $p_i$, then you have little hope of finding a triangulation or of proving the normality of the semigroup ring (which is what you are asking about). | |
| Feb 20, 2014 at 11:17 | comment | added | Per Alexandersson | I can find the vertices explicitly. I checked the condition on all vertices having the same degree, but this is not true in general, so they are not smooth. Finding a triangulation in general is too hard in my case i believe; a priori, not even the number of vertices is easy to find (unless the polytope is integral, but then I can only do it by checking all vertices explicitly...) Can you give an explicit family of polytopes that satisfy your conditions, but not being too trivial (say, hypercubes)? | |
| Feb 20, 2014 at 2:25 | history | answered | Lev Borisov | CC BY-SA 3.0 |