Abstract
We introduce an extension of the Parikh mapping called the Parikh q-matrix mapping, which takes its values in matrices with polynomial entries. The morphism constructed represents a word ω over a κ-letter alphabet as a κ-dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable q. We show that by appropriately embedding the κ-letter alphabet into the κ+1)-letter alphabet and putting q=1, we obtain the extension of the Parikh mapping to (κ+1)-dimensional (numerical)matrices introduced by Mateescu, Salomaa, Salomaa, and Yu. The Parikh q-matrix mapping however, produces matrices that carry more information about ω than the numerical Parikh matrix. The entries of the q-matrix image of ω under this morphism is constructed by the q-counting number of occurrences of certain words as scattered subwords of ω
Work done in part while on sabbatical at Sabanci University, Istanbul, Turkey during 2003–2004.
Supported in part by NSF Grants IIS-0101134 and CCR02-08595.
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Egecioglu, O., Ibarra, O.H. (2004). A Matrix Q-Analogue of the Parikh Map. In: Levy, JJ., Mayr, E.W., Mitchell, J.C. (eds) Exploring New Frontiers of Theoretical Informatics. IFIP International Federation for Information Processing, vol 155. Springer, Boston, MA. https://doi.org/10.1007/1-4020-8141-3_12
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DOI: https://doi.org/10.1007/1-4020-8141-3_12
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