A connection between palindromic and factor complexity using return words

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 + 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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Michelangelo Bucci, Alessandro De Luca, Amy Glen, Luca Q. Zamboni
• Keywords: Complete Returns, CORR 2008, Education, Infinite Word, Palindromes