15 citations · 105 across the 66 of their papers we have counts for
11 papers · 1 filter
Words Avoiding Reversed Factors, Revisited
Lukas Fleischer, Jeffrey Shallit
In 2005, Rampersad and the second author proved a number of theorems about infinite words x with the property that if w is any sufficiently long finite factor of x, then its revers…
New Bounds on Antipowers in Words
Lukas Fleischer, Samin Riasat, Jeffrey Shallit
Fici et al. defined a word to be a k-power if it is the concatenation of k consecutive identical blocks, and an r-antipower if it is the concatenation of r pairwise distinct blocks…
Sum-free sets generated by the period-k-folding sequences and some Sturmian sequences
Jean-Paul Allouche, Jeffrey Shallit, Zhixiong Wen +2
First, we show that the sum-free set generated by the period-doubling sequence is not -regular for any . Next, we introduce a generalization of the period-doubling sequ…
Words With Few Palindromes, Revisited
Lukas Fleischer, Jeffrey Shallit
In 2013, Fici and Zamboni proved a number of theorems about finite and infinite words having only a small number of factors that are palindromes. In this paper we rederive some of…
Automatic sequences are also non-uniformly morphic
Jean-Paul Allouche, Jeffrey Shallit
It is well-known that there exist infinite sequences that are the fixed point of non-uniform morphisms, but not -automatic for any . In this note we show that every -autom…
Borders, Palindrome Prefixes, and Square Prefixes
Daniel Gabric, Jeffrey Shallit
We show that the number of length-n words over a k-letter alphabet having no even palindromic prefix is the same as the number of length-n unbordered words, by constructing an expl…