کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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426868 | 686325 | 2009 | 14 صفحه PDF | دانلود رایگان |

A generalized two-dimensional word is a function on Z2Z2 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 φ:Z2→Rnφ:Z2→Rn is a generalized centered function of radius r with the matrix A if∑y∈Z2:0<|y-x|⩽r-35ptφ(y)=φ(x)Afor every x∈Z2x∈Z2, where for x=(x1,x2)x=(x1,x2), y=(y1,y2)y=(y1,y2) we have |y-x|=|y1-x1|+|y2-x2||y-x|=|y1-x1|+|y2-x2|. We prove that every generalized centered function of radius r>1r>1 with a finite number of values is periodic. For r=1r=1 the existence of non-periodic generalized centered functions depends on the spectrum of the matrix A. Similar results are obtained for the infinite triangular and hexagonal grids.
Journal: Information and Computation - Volume 207, Issue 11, November 2009, Pages 1315–1328