# On the conjecture of unbounded palindromic length

In a 2013 paper with S. Puzynina and L. Zamboni, we stated the following conjecture: Let $w$ be an aperiodic infinite word, that is, a sequence of symbols not ending by an infinite repetition of the form $uuu\cdots$. Then for every $K>0$ there exists a prefix of $w$ which cannot be decomposed into a concatenation of less than $K$ different palindromes.

The conjecture stays unproven, but I will give a survey on recent advances on it and possible methods for the general proof.

## Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Anna Frid

## Speaker's Institution

Aix-Marseille University, France

## Area

Semigroups, Automata and Languages