4 papers
On a sequence of Kimberling and its relationship to the Tribonacci word
Lubomíra Dvořáková, Edita Pelantová, Jeffrey Shallit
In 2017, Clark Kimberling defined an interesting sequence of 's and 's by certain inflation rules, and he made a number of conjectures about thi…
The limit of repetition thresholds of rich sequences
Lubomíra Dvořáková, Edita Pelantová
The repetition threshold of a class of sequences is the smallest number such that a sequence from the class contains no repetition with exponent . We focus on the class $\…
Frequencies of letters in infinite -balanced sequences
Lubomíra Dvořáková, Edita Pelantová
Frequency of letters in a symbolic sequence over a finite alphabet is one of the basic characteristics of . The notion of -balancedness captures the property…
On two conjectures of Shallit about Thue-Morse-like sequences
Lubomíra Dvořáková, Savinien Kreczman, Edita Pelantová
We study a class of infinite words , where is a positive integer, recently introduced by J. Shallit. This class includes the Thue-Morse sequence , the Fibonacci-Thue…