Reducing the ambiguity of Parikh matrices
Jeff Dick
Laura Hutchinson
Robert Mercas
Daniel Reidenbach
2134/11297906.v1
https://repository.lboro.ac.uk/articles/conference_contribution/Reducing_the_ambiguity_of_Parikh_matrices/11297906
The Parikh matrix mapping allows us to describe words using matrices. Although compact, this description comes with a level of ambiguity since a single matrix may describe multiple words. This work looks at how considering the Parikh matrices of various transformations of a given word can decrease that ambiguity. More specifically, for any word, we study the Parikh matrix of its Lyndon conjugate as well as that of its projection to a smaller alphabet. Our results demonstrate that ambiguity can often be reduced using these concepts, and we give conditions on when they succeed.<br>
2019-11-29 13:43:28
Combinatorics
Parikh matrix
Ambiguity
Lyndon conjugate