Parikh Matrices: Subword Indicators and Degrees of Ambiguity

Abstract

The quantity \(|w|_{u}\), the number of occurrences of a word u as a (scattered) subword of a word w gives important numerical information about the word w. Properly chosen values \(|w|_{u}\), for different u’s, characterize the word w completely. Certain upper triangular matrices, customarily referred to as Parikh matrices have turned out to be very useful for computing numbers \(|w|_{u}\). This partially expository paper discusses some highlights and open problems of the theory of Parikh matrices and subword occurrences. Special emphasis is on subword indicators and degrees of ambiguity.