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.
Mots clés : Parikh mapping, Parikh matrix, formal power series, Prouhet-Tarry-Escott problem, subword, amiable words
@article{ITA_2010__44_2_209_0, author = {\v{C}ern\'y, Anton}, title = {Generalizations of {Parikh} mappings}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {209--228}, publisher = {EDP-Sciences}, volume = {44}, number = {2}, year = {2010}, doi = {10.1051/ita/2009021}, mrnumber = {2674541}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita/2009021/} }
TY - JOUR AU - Černý, Anton TI - Generalizations of Parikh mappings JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2010 SP - 209 EP - 228 VL - 44 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2009021/ DO - 10.1051/ita/2009021 LA - en ID - ITA_2010__44_2_209_0 ER -
%0 Journal Article %A Černý, Anton %T Generalizations of Parikh mappings %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2010 %P 209-228 %V 44 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2009021/ %R 10.1051/ita/2009021 %G en %F ITA_2010__44_2_209_0
Černý, Anton. Generalizations of Parikh mappings. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 2, pp. 209-228. doi : 10.1051/ita/2009021. http://archive.numdam.org/articles/10.1051/ita/2009021/
[1] 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. | Zbl
and ,[2] Binary amiable words. Int. J. Found. Comput. Sci. 18 (2007) 387-400. | Zbl
,[3] Parikh matrices and amiable words. Theoret. Comput. Sci. 390 (2008) 102-109. | Zbl
, and ,[4] On the injectivity of the Parikh matrix mapping. Fund. Inform. 49 (2002) 289-299. | Zbl
, and ,[5] The origins of combinatorics on words. Eur. J. Combin. 28 (2007) 996-1022. | Zbl
and ,[6] A Survey of Modern Algebra. MacMillan, New York, 4th edn. (1977). | Zbl
and ,[7] The Prouhet-Tarry-Escott problem revisited. Enseign. Math. 40 (1994) 3-27. | Zbl
and ,[8] On fairness of D0L systems. Discrete Appl. Math. 155 (2007) 1769-1773. | Zbl
,[9] On subword symmetry of words. Int. J. Found. Comput. Sci. 19 (2008) 243-250. | Zbl
,[10] On fair words. J. Autom. Lang. Comb. 14 (2009) (to appear). | Zbl
,[11] 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.
and ,[12] Some characterizations of Parikh matrix equivalent binary words. Inform. Process. Lett. 92 (2004) 77-82. | Zbl
and ,[13] Combinatorics on words. Cambridge University Press (1997). | Zbl
,[14] 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) 170-180. | Zbl
,[15] Matrix indicators for subword occurrences and ambiguity. Int. J. Found. Comput. Sci. 15 (2004) 277-292. | Zbl
and ,[16] A sharpening of the Parikh mapping. RAIRO-Theor. Inf. Appl. 35 (2001) 551-564. | Numdam | Zbl
, , and ,[17] Subword histories and Parikh matrices. J. Comput. System Sci. 68 (2004) 1-21. | Zbl
, and ,[18] On context-free languages. J. ACM 13 (1966) 570-581. | Zbl
,[19] Mémoire sur quelques relations entre les puissances des nombres. C.R. Acad. Sci. Paris 33 (1851) 255.
,[20] Independence of certain quantities indicating subword occurrences. Theoret. Comput. Sci. 362 (2006) 222-231. | Zbl
,[21] Comparing subword occurrences in binary D0L sequences. Int. J. Found. Comput. Sci. 18 (2007) 1395-1406. | Zbl
,[22] A Salomaa, Subword balance in binary words, languages and sequences. Fund. Inform. 75 (2007) 469-482. | Zbl
[23] Extending Parikh matrices. Theoret. Comput. Sci. 310 (2004) 233-246. | Zbl
,[24] Wikipedia. Rings. http://en.wikipedia.org/wiki/Ring_(mathematics).
Cité par Sources :