On Commuting Parikh q-Matrices

Article type: Research Article

Authors: Bera, Somnath^a | Mahalingam, Kalpana^{b; *}

Affiliations: [a] Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036 India. somnathbera89@gmail.com | [b] Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036 India. kmahalingam@iitm.ac.in

Correspondence: [*] Address for correspondence: Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036 India.

Abstract: This paper investigates properties of words such that their Parikh q-matrices commute. For any two words u, v ∈∑k*, the concept of q-weak ratio property between u and v is introduced. Based on this property a necessary and sufficient condition for the Parikh q-matrices of any two words over binary alphabet to commute is given. This paper also provides a special class of words over an arbitrary alphabet ∑k such that their Parikh q-matrices commute.

Keywords: Parikh q-matrix mapping, commutativity, q-ambiguity, q-weak ratio property

DOI: 10.3233/FI-2020-1907

Journal: Fundamenta Informaticae, vol. 172, no. 4, pp. 327-341, 2020