Multidimensional unrepetitive configurations
An existence of bi-finite words on finite alphabets which are r-th power- free together with a certain class of their subwords is used for an effective construction of the following n-dimensional configuration: It is possible to associate with each lattice-point of the n-dimensional space a letter of a finite alphabet so that the sequences of the letters corresponding to the points lying on a same straight line are r-th power- free words \((r>1)\). An analogous result is obtained also for some avoidable sets of patterns.
scientific article; zbMATH DE number 4060746