A connection between palindromic and factor complexity using return words

Details A connection between palindromic and factor complexity using return words A connection between palindromic and factor complexity using return words

2008-02-10

arxiv.org/abs/0802.1332v2

Advances In Applied Mathematics 42 (2009) 60--74

Mathematics

Combinatorics

17 pages; minor adjustment to the main theorem and other minor changes (particularly in Sections 3 and 4); accepted by "Advanc

Scientific paper

10.1016/j.aam.2008.03.005

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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