2018/12/10 by Kateřina Medková, Edita Pelantová, Medková, Kateřina +3
Computer Science · Engineering · #65R15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1812.03748
openalex publication_date 2018/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Complementary symmetric Rote sequences are binary sequences which have factor complexity C(n) = 2n for all integers n ≥ 1 and whose languages are closed under the exchange of letters. These sequences are intimately linked to Sturmian sequences. Using this connection we investigate the return words and the derivated sequences to the prefixes of any complementary symmetric Rote sequence v which is associated with a standard Sturmian sequence u. We show that any non-empty prefix of v has three return words. We prove that any derivated sequence of v is coding of three interval exchange transformation and we determine the parameters of this transformation. We also prove that v is primitive substitutive if and only if u is primitive substitutive. Moreover, if the sequence u is a fixed point of a primitive morphism, then all derivated sequences of v are also fixed by primitive morphisms. In that case we provide an algorithm for finding these fixing morphisms.