On periodicity of two-dimensional words
نویسندگان
چکیده
A two-dimensional word is a function on Z 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.
منابع مشابه
Properties of Two-Dimensional Words
Combinatorics on words in one dimension is a well-studied subfield of theoretical computer science with its origins in the early 20th century. However, the closely-related study of twodimensional words is not as popular, even though many results seem naturally extendable from the one-dimensional case. This thesis investigates various properties of these twodimensional words. In the early 1960s,...
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 391 شماره
صفحات -
تاریخ انتشار 2008