Gabriele Fici

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math.CO2025

Generalized De Bruijn Words, Invertible Necklaces, and the Burrows-Wheeler Transform

Gabriele Fici, Estéban Gabory

We define generalized de Bruijn words as those words having a Burrows-Wheeler transform that is a concatenation of permutations of the alphabet. We show that generalized de Bruijn…

math.CO2024

The Shortest Interesting Binary Words

Gabriele Fici

I will show that there exist two binary words (one of length 4 and one of length 6) that play a special role in many different problems in combinatorics on words. They can therefor…

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…