A connection between palindromic and factor complexity using return words

Bucci, Michelangelo; De Luca, Alessandro; Glen, Amy; Zamboni, Luca Q.

doi:10.1016/j.aam.2008.03.005

arXiv 2008-02-10 DOI 10.1016/j.aam.2008.03.005 2 مشاهدة

A connection between palindromic and factor complexity using return words

Bucci, Michelangelo · De Luca, Alessandro · Glen, Amy · Zamboni, Luca Q.

Combinatorics Discrete Mathematics 68R15

الأصل · EN

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.

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