On Palindromic Length of Sturmian Sequences

摘要

Frid, Puzynina and Zamboni (2013) defined the palindromic length of a finite word w as the minimal number of palindromes whose concatenation is equal to w. For an infinite word u we study palu, that is, the function that assigns to each positive integer n, the maximal palindromic length of factors of length n in u. Recently, Frid (2018) proved that lim sup_(n→∞) pal_u (n) = +∞ for any Sturmian word u. We show that there is a constant K > 0 such that palu (n) ≤ K In n for every Sturmian word w, and that for each non-decreasing function f with property lim_(n→∞) f(n) = +∞ there is a Sturmian word u such that pal_u(n) =O(f(n)).