Dvořáková, Lubomíra and Medková, Kateřina and Pelantová, Edita - Complementary symmetric Rote sequences: the critical exponent and the recurrence function

dmtcs:6204 - Discrete Mathematics & Theoretical Computer Science, June 6, 2020, vol. 22 no. 1 - https://doi.org/10.23638/DMTCS-22-1-20
Complementary symmetric Rote sequences: the critical exponent and the recurrence function

Authors: Dvořáková, Lubomíra and Medková, Kateřina and Pelantová, Edita

We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions associated with the S-adic representations of the corresponding standard Sturmian sequences. The results are based on a thorough study of return words to bispecial factors of Sturmian sequences. Using the formula for the critical exponent, we describe all complementary symmetric Rote sequences with the critical exponent less than or equal to 3, and we show that there are uncountably many complementary symmetric Rote sequences with the critical exponent less than the critical exponent of the Fibonacci sequence. Our study is motivated by a~conjecture on sequences rich in palindromes formulated by Baranwal and Shallit. Its recent solution by Curie, Mol, and Rampersad uses two particular complementary symmetric Rote sequences.


Volume: vol. 22 no. 1
Section: Combinatorics
Published on: June 6, 2020
Submitted on: March 17, 2020
Keywords: Mathematics - Combinatorics,68R15


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