A connection between palindromic and factor complexity using return words
Combinatorics
2010-04-08 v2 Discrete Mathematics
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.
Cite
@article{arxiv.0802.1332,
title = {A connection between palindromic and factor complexity using return words},
author = {Michelangelo Bucci and Alessandro De Luca and Amy Glen and Luca Q. Zamboni},
journal= {arXiv preprint arXiv:0802.1332},
year = {2010}
}
Comments
17 pages; minor adjustment to the main theorem and other minor changes (particularly in Sections 3 and 4); accepted by "Advances in Applied Mathematics"