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Generalizations of Parikh mappings

Published online by Cambridge University Press:  16 December 2009

Anton Černý*
Affiliation:
Department of Information Science, Kuwait University, P.O. Box 5969 Safat 13060, Kuwait; [email protected]
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Abstract

Parikh matrices have become a useful tool for investigation of subword structure of words. Several generalizations of this concept have been considered. Based on the concept of formal power series, we describe a general framework covering most of these generalizations. In addition, we provide a new characterization of binary amiable words – words having a common Parikh matrix.

Type
Research Article
Copyright
© EDP Sciences, 2010

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References

J.-P. Allouche and J.O. Shallit, The ubiquitous Prouhet-Thue-Morse sequence, in Sequences and Their Applications, Proceedings of SETA '98, edited by C. Ding, T. Helleseth and H. Niederreiter. Springer-Verlag (1999) 1–16.
Atanasiu, A., Binary amiable words. Int. J. Found. Comput. Sci. 18 (2007) 387400. CrossRef
Atanasiu, A., Atanasiu, R. and Petre, I., Parikh matrices and amiable words. Theoret. Comput. Sci. 390 (2008) 102109. CrossRef
Atanasiu, A., Martín-Vide, C. and Mateescu, A., On the injectivity of the Parikh matrix mapping. Fund. Inform. 49 (2002) 289299.
Berstel, J. and Perrin, D., The origins of combinatorics on words. Eur. J. Combin. 28 (2007) 9961022. CrossRef
G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra. MacMillan, New York, 4th edn. (1977).
Borwein, P. and Ingalls, C., The Prouhet-Tarry-Escott problem revisited. Enseign. Math. 40 (1994) 327.
Černý, A., On fairness of D0L systems. Discrete Appl. Math. 155 (2007) 17691773. CrossRef
Černý, A., On subword symmetry of words. Int. J. Found. Comput. Sci. 19 (2008) 243250. CrossRef
A. Černý, On fair words. J. Autom. Lang. Comb. 14 (2009) (to appear).
Ö. Eğecioğlu and O.H. Ibarra, A matrix q-analogue of the Parikh mapping, in IFIP TCS, edited by J.-J. Lévy, E.W. Mayr and J.C. Mitchell. Kluwer (2004) 125–138.
S. Fossé and G. Richomme, Some characterizations of Parikh matrix equivalent binary words. Inform. Process. Lett. 92 (2004) 77–82.
M. Lothaire, Combinatorics on words. Cambridge University Press (1997).
Mateescu, A., Algebraic aspects of Parikh matrices, in Theory Is Forever, edited by J. Karhumäki, H.A. Maurer, G. Păun and G. Rozenberg. Lect. Notes Comput. Sci. 3113 (2004) 170180. CrossRef
Mateescu, A. and Salomaa, A., Matrix indicators for subword occurrences and ambiguity. Int. J. Found. Comput. Sci. 15 (2004) 277292. CrossRef
Mateescu, A., Salomaa, A., Salomaa, K. and Yu, S., A sharpening of the Parikh mapping. RAIRO-Theor. Inf. Appl. 35 (2001) 551564. CrossRef
Mateescu, A., Salomaa, A. and Sheng Yu, Subword histories and Parikh matrices. J. Comput. System Sci. 68 (2004) 121. CrossRef
Parikh, R.J., On context-free languages. J. ACM 13 (1966) 570581. CrossRef
Prouhet, E., Mémoire sur quelques relations entre les puissances des nombres. C.R. Acad. Sci. Paris 33 (1851) 255.
Salomaa, A., Independence of certain quantities indicating subword occurrences. Theoret. Comput. Sci. 362 (2006) 222231. CrossRef
Salomaa, A., Comparing subword occurrences in binary D0L sequences. Int. J. Found. Comput. Sci. 18 (2007) 13951406. CrossRef
Salomaa, A, Subword balance in binary words, languages and sequences. Fund. Inform. 75 (2007) 469482.
Şerbănuţă, T.-F., Extending Parikh matrices. Theoret. Comput. Sci. 310 (2004) 233246. CrossRef
Wikipedia. Rings. http://en.wikipedia.org/wiki/Ring_(mathematics).