Extensions of rich words
arXiv:1312.4350 · doi:10.1016/j.tcs.2014.06.033
Abstract
In [X. Droubay et al, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has at most |w|+1 many distinct palindromic factors, including the empty word. The unified study of words which achieve this limit was initiated in [A. Glen et al, Palindromic richness, Eur. Jour. of Comb. 30 (2009)]. They called these words rich (in palindromes). This article contains several results about rich words and especially extending them. We say that a rich word w can be extended richly with a word u if wu is rich. Some notions are also made about the infinite defect of a word, the number of rich words of length n and two-dimensional rich words.
19 pages, 3 figures
References in corpus (1)
Cited by in corpus (9)
- On Number of Rich Words
- Upper Bound for Palindromic and Factor Complexity of Rich Words
- The repetition threshold for binary rich words
- A Unique Extension of Rich Words
- Repetitions in infinite palindrome-rich words
- On Words with the Zero Palindromic Defect
- Construction Of A Rich Word Containing Given Two Factors
- Palindromic factorization of rich words
- Double-Ended Palindromic Trees in Linear Time