Jeffrey Shallit

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20132026

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math.CO2026

Repetition Avoidance in Curling-Number Transforms

Geoffrey Caveney, Haoxuan, Dong +1

We study repetition avoidance in a word $w$ and its curling-number transform $C (w)$ . For alphabets of sizes $2$ , $3$ , and $4$ , we use Thue-Morse-based morphic construct…

math.CO2026

Palindrome complexity versus factor complexity

Jeffrey Shallit

Let $x = (a_{i})_{i \geq 0}$ be an infinite word over a finite alphabet $Σ$ . Let $ρ (n)$ be the factor complexity function for $x$ and $Pal (n)$ be the palindrome compl…

math.CO2026

Ten Squares Force an Overlap

Jeffrey Shallit

We prove that every concatenation of $10$ or more binary squares contains an overlap. The bound $10$ is best possible. In contrast, over a ternary alphabet, there are infinitely lo…

cs.FL2026

Complexity of Linear Subsequences of Fibonacci-Automatic Sequences

Delaram Moradi, Narad Rampersad, Jeffrey Shallit

We construct automata with input(s) in Fibonacci representation (also known as Zeckendorf representation) recognizing some basic arithmetic relations and study their number of stat…