arXiv subjects

Mickaël Postic

Publications and source records attributed to Mickaël Postic.

2 recordsLinked to original sources

arXiv2019

Anti-Powers in Primitive Uniform Substitutions

In a recent work, A. Berger and C. Defant showed that if $x$ is a fixed point of a binary uniform and primitive morphism, then there exists a constant $C$ such that for all positive integers $i,k,$ beginning in position $n$ in $x$ is a $k$-anti-power with block length at most $Ck$. They ask whether this result extends to a broader class of morphic words. In this note we extend their results to fixed points of uniform primitive morphisms on arbitrary finite alphabets. Our methods make use of the recognisability of uniform primitive morphisms. This result was proved independantly by S. Garg, using a different technique.

math.CO↗

arXiv2019

$ω$-Lyndon words

Let $\A$ be a finite non-empty set and $\preceq $ a total order on $\A^\nats$ verifying the following lexicographic like condition: For each $n\in \nats$ and $u, v\in \A^n,$ if $u^ω\prec v^ω$ then $ux\prec vy$ for all $x, y \in \A^\nats.$ A word $x\in \A^\nats$ is called $ω$-Lyndon if $x\prec y$ for each proper suffix $y$ of $x.$ A finite word $w\in \A^+$ is called $ω$-Lyndon if $w^ω\prec v^ω$ for each proper suffix $v$ of $w.$ In this note we prove that every infinite word may be written uniquely as a non-increasing product of $ω$-Lyndon words.

math.CO↗