Parikh matrices and amiable words

Authors:
Adrian Atanasiu;Radu Atanasiu;Ion Petre
Affiliations:
Faculty of Mathematics and Computer Science, Bucharest University, Str. Academiei 14, Bucharest 010014, Romania;MSC, Bucharest University, Romania;Academy of Finland, Finland and Department of IT, bo Akademi University, Turku 20520, Finland
Venue:
Theoretical Computer Science
Year:
2008

Citing 6
Cited 3

On Context-Free Languages

Journal of the ACM (JACM)
Handbook of Formal Languages

Handbook of Formal Languages
On the injectivity of the Parikh matrix mapping

Fundamenta Informaticae
Some characterizations of Parikh matrix equivalent binary words

Information Processing Letters
Independence of certain quantities indicating subword occurrences

Theoretical Computer Science
A Low-complexity Distance for DNA Strings

Fundamenta Informaticae

Subword histories and associated matrices

Theoretical Computer Science
Criteria for the matrix equivalence of words

Theoretical Computer Science
Binary images, M-vectors, and ambiguity

IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis

Quantified Score

Hi-index	5.23

Visualization

Abstract

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words with the same Parikh matrix; these words are called ''amiable''. The presented results extend the results obtained in [A. Atanasiu, Binary amiable words, Int. J. Found. Comput. Sci. 18 (2) (2007) 387-400] for the binary case. In particular it is shown that all the words having the same Parikh matrix can be obtained one from another by applying only two types of transformations. Moreover, the mirrors of two amiable words are also amiable (thus forming a symmetrical class of words).