On fair words

Authors:
Anton Černý
Affiliations:
Department of Information Science, Kuwait University, Kuwait
Venue:
Journal of Automata, Languages and Combinatorics
Year:
2009

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Abstract

A word is called fair if it contains, for each pair of distinct symbols a, b, the same number of occurrences of the scattered subword ab as of ba. We provide formulas for the number of fair words of length up to 10 on a k-letter alphabet and some methods for constructing fair words. We use a generalization of Parikh vector called p-matrix to count the number of occurrences of subwords of shape ab in a word.