Complexity of cutting words on regular tilings
The authors study the cutting words, and they investigate cutting lines on a regular tiling by computing the complexity of the infinite cutting word \(u\) and find the complexity of cutting words for each regular tiling by translation of one polyomino. Finally there is shown the complexity of a cutting word \(u\) in a regular tiling with a polyomino \(Q\) which is equal to \(P_n(u)=(p+q-1)n+1\) for all \(n\geq 0\), where \(P_n(u)\) counts the number of distinct factors of length \(n\) of the infinite word \(u\) and where the boundary of \(Q\) is constructed of \(2p\) horizontal and \(2q\) vertical unit segments. But as said in the conclusion, many questions remain open.
scientific article; zbMATH DE number 5077717
scientific article