A Matrix q-Analogue of the Parikh Map

We introduce an extension of the Parikh mapping called the Parikh ¢ -matrix mapping, which takes its values in matrices with polynomial entries. The morphism constructed represents a word £ over a ¤ -letter alphabet as a ¤ -dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable ¢ . We show that by appropriately embedding the ¤ -letter alphabet into the ¥¦¤¨§© -letter alphabet and putting ¢© , we obtain the extension of the Parikh mapping to ¥¦¤§© -dimensional (numerical) matrices introduced by Mateescu, Salomaa, Salomaa, and Yu. The Parikh ¢ -matrix mapping however, produces matrices that carry more information about £ than the numerical Parikh matrix. The entries of the ¢ -matrix image of £ under this morphism is constructed by ¢ -counting the number of occurrences of certain words as scattered subwords of £ .

• Type: Conference
• Year: 2004
• Where: IFIP
• Authors: Ömer Egecioglu, Oscar H. Ibarra
• Keywords: -letter Alphabet, Communications, IFIPTCS 2004, Parikh, Parikh Mapping