On the Number of Neighbors in Normal Tiling
Longxiu Huang, Tao Wang · SIAM Journal on Discrete Mathematics · 2017
The paper is devoted to the normal tiling whose tiles are uniformly bounded and general connected closed sets instead of being restricted to polytopes or convex sets. We estimate the number of neighbors of a tile in the normal tiling and develop various novel techniques to derive lower and upper bounds. The bounds for lattice tilings are shown to be optimal.