On periodicity of generalized two-dimensional infinite words
A generalized two-dimensional word is a function oil Z(2) with a finite number of values. The main problem we are interested in is periodicity of two-dimensional words satisfying some local conditions. Let A be a matrix of order n. The function phi : Z(2) -> R-n is a generalized centered function of radius r with the matrix A if Sigma(y is an element of z2:0  1 with a finite number of values is periodic. For r = 1 the existence of non-periodic generalized centered functions depends oil the spectrum of the matrix A. Similar results are obtained for the infinite triangular and hexagonal grids. (C) 2009 Elsevier Inc. All rights reserved.
periodicity bidimensional word perfect coloring equitable partition nivat's conjecture