Chern, Z. J.; Teh, W. C. Extension of Parikh matrices to terms and its injectivity problem. (English) Zbl 1434.68381 Malays. J. Math. Sci. 13, Spec. Iss.: 3rd International Conference on Mathematical Sciences and Statistics (ICMSS2018), 147-156 (2019). Summary: Parikh matrices introduced by A. Mateescu et al. [Theor. Inform. Appl. 35, No. 6, 551–564 (2001; Zbl 1005.68092)] are very useful in understanding structural properties of words by analyzing their numerical properties. This is due to the information of a word provided by its Parikh matrix is more than its Parikh vector. The study of Parikh matrices is extended in this paper to terms formed over a signature with a binary underlying alphabet. We obtain some numerical properties that characterize when a word is a term. Finally, new \(M\)-equivalence preserving rewriting rules are introduced and shown to characterize \(M\)-equivalence for our terms, thus contributing towards the injectivity problem. Cited in 1 Document MSC: 68R15 Combinatorics on words 05A05 Permutations, words, matrices Keywords:injectivity problem; \(M\)-equivalence; Parikh matrices; subword; terms Citations:Zbl 1005.68092 PDFBibTeX XMLCite \textit{Z. J. Chern} and \textit{W. C. Teh}, Malays. J. Math. Sci. 13, 147--156 (2019; Zbl 1434.68381) Full Text: Link