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On the Injectivity of the Parikh Matrix Mapping

100%

Atanasiu A. , Martin-Vide C. , Mateescu A.

tom Vol. 49, nr 4

289-299

In this paper we investigate the injectivity of the Parikh matrix mapping. This research is done mainly on the binary alphabet. We identify a family of binary words, refered to as ``palindromic amiable'', such that two such words are palindromic amiable if and only if they have the same image by the Parikh matrix mapping. Some other related problems are discussed, too.

Subword Balance in Binary Words, Languages and Sequences

75%

Salomaa A.

tom Vol. 75, nr 1-4

4690482-4690482

We investigate binary words and languages having a balanced structure of (scattered) subwords. We introduce a "difference function" D for binary words. For D=0, the resulting language is properly context-sensitive. Parikh matrices constitute a useful technical tool in the study, we investigate also the independence of their entries. The investigation is extended to concern w-words and periodicity. For the Fibonacci word, the D-values are in many ways connected with the Fibonacci numbers.