Jeffrey Shallit

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20242026

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7 papers · 1 filter

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…

math.CO2025

The Narayana Morphism and Related Words

Jeffrey Shallit

The Narayana morphism $ν$ 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 this…

math.CO2024

Some Remarks on Palindromic Periodicities

Gabriele Fici, Jeffrey Shallit, Jamie Simpson

We say a finite word $x$ is a palindromic periodicity if there exist two palindromes $p$ and $s$ such that $∣ x ∣ \geq ∣ p s ∣$ and $x$ is a prefix of the word $(p s)^{ω} = p s p s p s \dots$ . I…

math.CO2024

Consecutive Power Occurrences in Sturmian Words

Jason Bell, Chris Schulz, Jeffrey Shallit

We show that every Sturmian word has the property that the distance between consecutive ending positions of cubes occurring in the word is always bounded by $10$ and this bound is…