Complementary symmetric Rote sequences: the critical exponent and the recurrence function
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1
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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.
@article{DMTCS_2020_22_1_a16,
author = {Dvo\v{r}\'akov\'a, Lubom{\'\i}ra and Medkov\'a, Kate\v{r}ina and Pelantov\'a, Edita},
title = {Complementary symmetric {Rote} sequences: the critical exponent and the recurrence function},
journal = {Discrete mathematics & theoretical computer science},
publisher = {mathdoc},
volume = {22},
number = {1},
year = {2020-2021},
doi = {10.23638/DMTCS-22-1-20},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-20/}
}
TY - JOUR AU - Dvořáková, Lubomíra AU - Medková, Kateřina AU - Pelantová, Edita TI - Complementary symmetric Rote sequences: the critical exponent and the recurrence function JO - Discrete mathematics & theoretical computer science PY - 2020-2021 VL - 22 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-20/ DO - 10.23638/DMTCS-22-1-20 LA - en ID - DMTCS_2020_22_1_a16 ER -
%0 Journal Article %A Dvořáková, Lubomíra %A Medková, Kateřina %A Pelantová, Edita %T Complementary symmetric Rote sequences: the critical exponent and the recurrence function %J Discrete mathematics & theoretical computer science %D 2020-2021 %V 22 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-20/ %R 10.23638/DMTCS-22-1-20 %G en %F DMTCS_2020_22_1_a16
Dvořáková, Lubomíra; Medková, Kateřina; Pelantová, Edita. Complementary symmetric Rote sequences: the critical exponent and the recurrence function. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1. doi: 10.23638/DMTCS-22-1-20
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