eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2020-06-06
vol. 22 no. 1
Combinatorics
10.23638/DMTCS-22-1-20
6204
journal article
Complementary symmetric Rote sequences: the critical exponent and the recurrence function
Lubomíra Dvořáková
Kateřina Medková
Edita Pelantová
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.
https://dmtcs.episciences.org/6204/pdf
Mathematics - Combinatorics
68R15