Properties of Parikh Matrices of Binary Words Obtained by an Extension of a Restricted Shuffle Operator

Abstract

We introduce an extension of the restricted shuffle operator on binary words considered by Atanasiu and Teh (2016). We then derive properties on Parikh matrix equivalence of words over a binary alphabet based on this extended shuffle operator and a weak-ratio property of words. We also examine the recently introduced concept of core Parikh matrix equivalence of binary words in the context of the restricted shuffle operator.