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Results tagged with nt.number-theory
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user 20186
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
1
vote
Number of *distinct* dot products of an integer vector by elements of a hyper-rectangle
Just as with the Subset-sum problem, there are decent methods for calculating your set $P$ that will be much better than brute force. If $S_k=\{\mathbf{u}\in S:u_i=0\text{ for all } i>k\}$ and $P_k=\{ …
- 5,971
7
votes
There are at most four mutually visible lattice points—?
(Inspired by a meta thread on answers given in comments, I am recapping the answer given in the comments (1 2 3) as a CW answer.)
The largest number of mutually visible points in $\mathbb{Z}^d$ is $2^ …
11
votes
4
answers
446
views
Sequential addition of points on a circle, optimizing asymptotic packing radius
Suppose I have to put $N$ points $x_1, x_2, \ldots, x_N$ on the circle $S^1$ of length 1 so as to achieve the largest minimum separation (packing radius). The optimal solution is the equally spaced ar …
- 5,971
5
votes
Sequential addition of points on a circle, optimizing asymptotic packing radius
Thinking more about Christian's stingy process, I have a new conjecture for the optimal $\mu$. I motivate the conjecture by modeling the evolution of the distribution of empty interval lengths in the …
- 5,971