ON THE PERMUTATIONS GENERATED BY STURMIAN WORDS
M. A. Makarov
UDC 519.1
Abstract: Infinite permutations of use in this article were introduced in [1]. Here we distinguish the
class of infinite permutations that are generated by the Sturmian words and inherit their properties.
We find the combinatorial complexity of these permutations, describe their Rauzy graphs, frequencies
of subpermutations, and recurrence functions. We also find their arithmetic complexity and Kamae
complexity.
Keywords: infinite permutation, Sturmian word, combinatorial complexity, Rauzy graph, arithmetic
complexity, Kamae complexity