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Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
5
votes
The Gauss circle problem on a hexagonal lattice
By using a transformation, it is possible to give a counting formula for the hexagonal lattice, similar to the formula on MathWolf. Here are the details.
Suppose your lattice is given by $\Lambda=T(\ …
3
votes
On the joints problem in finite fields
I know I'm digging up an old thread, but I figured out how to extend Kaplan, Sharir and Shustin's proof (similar to Quilodran's proof) to finite fields last summer, then later realized that Dvir indic …