Jeffrey Shallit

collaborators

5 papers

math.CO2026

Palindrome complexity versus factor complexity

Jeffrey Shallit

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

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…

math.CO2025

The Narayana Morphism and Related Words

Jeffrey Shallit

The Narayana morphism $I^½$ maps $0 \to 01$ , $1 \to 2$ , $2 \to 0$ and has a fixed point $n = n_{0} n_{1} n_{2} \dots = 0120010120120 \dots$ . In thi…

math.NT2025

The Hurt-Sada Array and Zeckendorf Representations

Jeffrey Shallit

Wesley Ivan Hurt and Ali Sada both independently proposed studying an infinite array where the $0$ 'th row consists of the non-negative integers $0, 1, 2, \dots$ in increasing order.…