# Generalizations of Parikh mappings

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 44, Issue: 2, page 209-228
- ISSN: 0988-3754

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topČerný, Anton. "Generalizations of Parikh mappings." RAIRO - Theoretical Informatics and Applications 44.2 (2010): 209-228. <http://eudml.org/doc/250762>.

@article{Černý2010,

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.
},

author = {Černý, Anton},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Parikh mapping; Parikh matrix; formal power series; Prouhet-Tarry-Escott
problem; subword; amiable words; Prouhet-Tarry-Escott problem},

language = {eng},

month = {5},

number = {2},

pages = {209-228},

publisher = {EDP Sciences},

title = {Generalizations of Parikh mappings},

url = {http://eudml.org/doc/250762},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Černý, Anton

TI - Generalizations of Parikh mappings

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/5//

PB - EDP Sciences

VL - 44

IS - 2

SP - 209

EP - 228

AB -
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.

LA - eng

KW - Parikh mapping; Parikh matrix; formal power series; Prouhet-Tarry-Escott
problem; subword; amiable words; Prouhet-Tarry-Escott problem

UR - http://eudml.org/doc/250762

ER -

## References

top- 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. Zbl1005.11005
- A. Atanasiu, Binary amiable words. Int. J. Found. Comput. Sci.18 (2007) 387–400. Zbl1123.68097
- A. Atanasiu, R. Atanasiu and I. Petre, Parikh matrices and amiable words. Theoret. Comput. Sci.390 (2008) 102–109. Zbl1134.68027
- A. Atanasiu, C. Martín-Vide and A. Mateescu, On the injectivity of the Parikh matrix mapping. Fund. Inform.49 (2002) 289–299. Zbl0997.68075
- J. Berstel and D. Perrin, The origins of combinatorics on words. Eur. J. Combin.28 (2007) 996–1022. Zbl1111.68092
- G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra. MacMillan, New York, 4th edn. (1977). Zbl0863.00001
- P. Borwein and C. Ingalls, The Prouhet-Tarry-Escott problem revisited. Enseign. Math.40 (1994) 3–27. Zbl0810.11016
- A. Černý, On fairness of D0L systems. Discrete Appl. Math.155 (2007) 1769–1773. Zbl1127.68048
- A. Černý, On subword symmetry of words. Int. J. Found. Comput. Sci.19 (2008) 243–250. Zbl1155.68033
- A. Černý, On fair words. J. Autom. Lang. Comb.14 (2009) (to appear). Zbl1205.68271
- 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. Zbl1066.68067
- S. Fossé and G. Richomme, Some characterizations of Parikh matrix equivalent binary words. Inform. Process. Lett. 92 (2004) 77–82. Zbl1173.68550
- M. Lothaire, Combinatorics on words. Cambridge University Press (1997). Zbl0874.20040
- A. Mateescu, 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. Zbl1055.68074
- A. Mateescu and A. Salomaa, Matrix indicators for subword occurrences and ambiguity. Int. J. Found. Comput. Sci.15 (2004) 277–292. Zbl1067.68117
- A. Mateescu, A. Salomaa, K. Salomaa and S. Yu, A sharpening of the Parikh mapping. RAIRO-Theor. Inf. Appl.35 (2001) 551–564. Zbl1005.68092
- A. Mateescu, A. Salomaa and Sheng Yu, Subword histories and Parikh matrices. J. Comput. System Sci.68 (2004) 1–21. Zbl1072.68085
- R.J. Parikh, On context-free languages. J. ACM13 (1966) 570–581. Zbl0154.25801
- E. Prouhet, Mémoire sur quelques relations entre les puissances des nombres. C.R. Acad. Sci. Paris33 (1851) 255.
- A. Salomaa, Independence of certain quantities indicating subword occurrences. Theoret. Comput. Sci.362 (2006) 222–231. Zbl1100.68058
- A. Salomaa, Comparing subword occurrences in binary D0L sequences. Int. J. Found. Comput. Sci.18 (2007) 1395–1406. Zbl1183.68353
- A Salomaa, Subword balance in binary words, languages and sequences. Fund. Inform.75 (2007) 469–482. Zbl1108.68072
- T.-F. Şerbănuţă, Extending Parikh matrices. Theoret. Comput. Sci.310 (2004) 233–246. Zbl1071.68036
- Wikipedia. Rings. http://en.wikipedia.org/wiki/Ring_(mathematics).

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