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Results tagged with discrete-geometry
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user 38468
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
4
votes
Minimal area of non-planar lattice curves
For any $\mathbb Z_2$-valued function $f$ on the set of segments $[v,v+e_i]$ for $v\in \mathbb Z^3$ and $i=1,2,3$, and any $S$ that bounds $C$
$$
\sum_{P\in S}\sum_{edge\in P} f(edge)
$$
is independe …
- 5,186
0
votes
Examples of toric threefolds
If you are willing to work with smooth stacks, rather than smooth toric varieties (or alternatively consider toric varieties with quotient singularities) then it is definitely
possible.
Combinatoria …
- 5,186
3
votes
Three questions concerning lattice points on sphere surfaces
It is not really my area, but the answer to part 2 is that you are looking for the smallest $N$ such that there are exactly $8n-4$ ways of writing it in the form $a^2+b^2$.
If such $N$ is even but i …
- 5,186