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.
A connection between palindromic and factor complexity using return words / Michelangelo, Bucci; DE LUCA, Alessandro; Amy, Glen; Luca Q., Zamboni. - In: ADVANCES IN APPLIED MATHEMATICS. - ISSN 0196-8858. - 42:(2009), pp. 60-74. [10.1016/j.aam.2008.03.005]
A connection between palindromic and factor complexity using return words
DE LUCA, ALESSANDRO;
2009
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) + 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.| File | Dimensione | Formato | |
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