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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 matrices.
@article{ITA_2001__35_6_551_0,
author = {Mateescu, Alexandru and Salomaa, Arto and Salomaa, Kai and Yu, Sheng},
title = {A sharpening of the {Parikh} mapping},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {551--564},
publisher = {EDP-Sciences},
volume = {35},
number = {6},
year = {2001},
mrnumber = {1922295},
zbl = {1005.68092},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ITA_2001__35_6_551_0/}
}
TY - JOUR AU - Mateescu, Alexandru AU - Salomaa, Arto AU - Salomaa, Kai AU - Yu, Sheng TI - A sharpening of the Parikh mapping JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2001 SP - 551 EP - 564 VL - 35 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/item/ITA_2001__35_6_551_0/ LA - en ID - ITA_2001__35_6_551_0 ER -
%0 Journal Article %A Mateescu, Alexandru %A Salomaa, Arto %A Salomaa, Kai %A Yu, Sheng %T A sharpening of the Parikh mapping %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2001 %P 551-564 %V 35 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/item/ITA_2001__35_6_551_0/ %G en %F ITA_2001__35_6_551_0
Mateescu, Alexandru; Salomaa, Arto; Salomaa, Kai; Yu, Sheng. A sharpening of the Parikh mapping. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 6, pp. 551-564. http://geodesic.mathdoc.fr/item/ITA_2001__35_6_551_0/