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arXiv · 0802.1332

A connection between palindromic and factor complexity using return words

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

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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Michelangelo Bucci, Alessandro De Luca, Amy Glen, Luca Q. Zamboni. 2008-04-11. A connection between palindromic and factor complexity using return words. https://doi.org/10.1016/j.aam.2008.03.005

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