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Robert Mercaş

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11 papers
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11

TCS Journal 2025 Journal Article

Ternary is still good for Parikh matrices

  • Robert Mercaş
  • Wen Chean Teh

The focus of this work is the study of Parikh matrices with emphasis on two concrete problems. In the first part of our presentation we show that a conjecture by Dick at al. in 2021 only stands in the case of ternary alphabets, while providing counterexamples for larger alphabets. In particular, we show that the only type of distinguishability in the case of 3-letter alphabets is the trivial one. The second part of the paper builds on the notion of Parikh matrices for projections of words, discussed in the former part of this work, and answers, once more in the case of a ternary alphabet, a question posed by Atanasiu et al. in 2022 with regards to the minimal Hamming distance in between words sharing a congruency class.

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TCS Journal 2021 Journal Article

Reducing the ambiguity of Parikh matrices

  • Jeffery Dick
  • Laura K. Hutchinson
  • Robert Mercaş
  • Daniel Reidenbach

The Parikh matrix mapping allows us to describe words using matrices. Whilst compact, this description comes with a level of ambiguity since a single matrix may describe multiple words. In this paper, we investigate how considering the Parikh matrices of various transformations of a given word can decrease that ambiguity. More specifically, for any word, we study the Parikh matrix of its projection to a smaller alphabet as well as that of its Lyndon conjugate. Our results demonstrate that ambiguity can often be reduced using these concepts, and we give conditions on when they succeed.

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