On palindromic factorization of words.

: A Frid, S Puzynina, L Q Zamboni

: 2013

: Advances in Applied Mathematics

: 5

: 50

: 5

: 737

: 748

: 12

: 0196-8858

DOI: https://doi.org/10.1016/j.aam.2013.01.002

Given a finite word u, we define its palindromic length |u|_{pal} to be the least number n such that u=v_1v_2... v_n with each v_i a palindrome. We address the following open question: Does there exist an infinite non ultimately periodic word w and a positive integer P such that |u|_{pal}

P. In particular, the result holds for all the k-power-free words and for the Sierpinski word.