Factor frequencies in languages invariant under more symmetries

Abstract

The number of frequencies of factors of length $n+1$ in a recurrent aperiodic infinite word does not exceed $3Δ\C(n)$, where $Δ\C (n)$ is the first difference of factor complexity, as shown by Boshernitzan. Pelantová together with the author derived a better upper bound for infinite words whose language is closed under reversal. In this paper, we further diminish the upper bound for uniformly recurrent infinite words whose language is invariant under all elements of a finite group of symmetries and we prove the optimality of the obtained upper bound.

13 pages

References in corpus (2)

• Languages invariant under more symmetries: overlapping factors versus palindromic richness
• Infinite words rich and almost rich in generalized palindromes

Cited by in corpus (2)

• Palindromic richness for languages invariant under more symmetries
• Complexity and invariant measure of the period-doubling subshift