Kronecker Sequences with Many Distances
Kronecker Sequences with Many Distances
The three gap theorem states that for any α∈R and N∈N, the number of different gaps between consecutive nα( mod 1) for n∈{1,…,N} is at most 3. Biringer and Schmidt (2008) instead considered the distance from each point to its nearest neighbor, generalizing to higher dimensions. We denote the maximum …