Enriching Parikh matrix mappings

Abstract

In this paper, we define the Super-Parikh (S-Parikh) matrix mapping as an extension of the Parikh matrix mapping introduced by Mateescu et al. Like the Parikh matrix, the extension revolves around a certain type of square matrices, but instead of non-negative integers, its matrix-mapped elements are non-negative rationals (fractions). We study the basic properties of the newly defined formalism and later on we investigate the injectivity of the mapping. Also, we begin a search for the reverse mapping – that is a method for obtaining a word, given the S-Parikh matrix.

Keywords:

• Parikh matrix mapping
• Parikh vector
• Parikh mapping
• S-Parikh matrix mapping
• combinatorics on words

Keywords:

• 68R15
• 05A05
• 68R05
• 15A15

Acknowledgements

The authors wish to thank the referees for their helpful suggestions and comments.

Notes

Formally, and |β|=j−1. We will also say that if there is no k<j such that .