Reconstructing words from a fixed palindromic length sequence

To every word ω is associated a sequence Gω built by computing at each position i the length of its longest palindromic suffix. This sequence is then used to compute the palindromic defect of a finite word Ω defined by D(Ω) = |Ω|+1−|Pal(Ω)| where Pal(Ω) is the set of its palindromic factors. In this paper we exhibit some properties of this sequence and introduce the problem of reconstructing a word from GΩ. In particular we show that up to a relabelling the solution is unique for 2‐letter alphabets.

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