Abstract
Combinatorics We study properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
Highlights
A D0L word ω is an infinite word on a finite alphabet Σ which is a fixed point of a morphism φ : Σ∗ −→ Σ∗, i.e., ω = lim φn(a) for a ∈ Σ
We study properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find a precise formula for their complexity
In this paper we study infinite permutations generated by infinite D0L words
Summary
The subword complexity C(n) of a word ω is the number of distinct words of length n which occur in ω This function on infinite words has been studied in numerous papers; see, for instance, the survey Cassaigne and Nicolas (2010). To the definition of subword complexity of infinite words, we can introduce the factor complexity of a permutation as the number of its distinct subpermutations of a given length. Another complexity function called maximal pattern complexity of infinite permutations was investigated in Avgustinovich et al (2011).
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