A Note on Symmetries in the Rauzy Graph and Factor Frequencies
L. Balkova, E. Pelantova
TL;DR
This paper investigates the relationship between symmetries in Rauzy graphs and factor frequencies in infinite words with reversible languages, establishing an upper bound on the number of distinct factor frequencies.
Contribution
It introduces a new bound on the number of different factor frequencies in words with symmetric Rauzy graphs, linking combinatorial structure to frequency distribution.
Findings
Bound of 2C(n+1)-2C(n)+1 on distinct factor frequencies
Analysis of symmetries in Rauzy graphs for infinite words
Insights into factor frequency distribution in reversible languages
Abstract
We focus on infinite words with languages closed under reversal. If frequencies of all factors are well defined, we show that the number of different frequencies of factors of length n+1 does not exceed 2C(n+1)-2C(n)+1.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · DNA and Biological Computing