On periodicity of two-dimensional words

A two-dimensional word is a function on Z2 with finite number of values. The main problem we are interested in is periodicity of twodimensional words satisfying some local conditions. In this paper we prove that every bounded centered function on the infinite rectangular grid is periodic. A function is called centered if the sum of its values in every ball is equal to 0. Similar results are obtained for the infinite triangular and hexagonal grids.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: S. A. Puzynina, Sergey V. Avgustinovich
• Keywords: Infinite Rectangular Grid, Main Problem, TCS 2008, Theoretical Computer Science, Two-dimensional Word