A connection between palindromic and factor complexity using return words

摘要

In this paper we prove that for any infinite word w whose set of factors is closed under reversal. the following conditions are equivalent: (I) all complete returns to palindromes are palindromes: (II)P(n) + P(n + 1) - C(n) + 2 for all n. where P (resp. C) denotes the palindromic complexity (resp. factor complexity) function of w, which counts the number of distinct palindromic factors (resp. factors) of each length in w.