A sharpening of the Parikh mapping

Issue		RAIRO-Theor. Inf. Appl. Volume 35, Number 6, November-December 2001 A tribute to Aldo de Luca


Page(s)		551 - 564
DOI		10.1051/ita:2001131

DOI: 10.1051/ita:2001131

Theoret. Informatics Appl. 35, 551-564 (2001)

Alexandru Mateescu¹, Arto Salomaa², Kai Salomaa³ and Sheng Yu⁴

¹ Faculty of Mathematics, University of Bucharest, Academiei 14, Bucharest, Romania; alexmate@pcnet.pcnet.ro.
² Turku Centre for Computer Science, Lemminkäisenkatu 14, 20520 Turku, Finland asalomaa@utu.fi.
³ Department of Computing and Information Science, Queen's University, Kingston, Ontario K7L 3N6, Canada; ksalomaa@cs.queensu.ca.
⁴ Department of Computer Science, University of Western Ontario, London, Ontario N6A 5B7, Canada; syu@csd.uwo.ca.

(Received February 6, 2001. Revised December 20, 2001.)

Abstract
In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of .

Mathematics Subject Classification. 68Q45, 68Q70

Key words: Formal languages -- Parikh mapping -- scattered subwords.

© EDP Sciences 2001

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