A new characteristic property of rich words
arXiv:0807.2303 · doi:10.1016/j.tcs.2008.11.001
Abstract
Originally introduced and studied by the third and fourth authors together with J. Justin and S. Widmer in arXiv:0801.1656, rich words constitute a new class of finite and infinite words characterized by containing the maximal number of distinct palindromes. Several characterizations of rich words have already been established. A particularly nice characteristic property is that all 'complete returns' to palindromes are palindromes. In this note, we prove that rich words are also characterized by the property that each factor is uniquely determined by its longest palindromic prefix and its longest palindromic suffix.
6 pages
References in corpus (4)
Cited by in corpus (18)
- Episturmian words: a survey
- On the least number of palindromes contained in an infinite word
- Extensions of rich words
- On Theta-palindromic Richness
- Infinite Words with Finite Defect
- Palindromic richness for languages invariant under more symmetries
- On Number of Rich Words
- Upper Bound for Palindromic and Factor Complexity of Rich Words
- Morphic images of episturmian words having finite palindromic defect
- Lambda Words: A Class of Rich Words Defined Over an Infinite Alphabet
- A Unique Extension of Rich Words
- Repetitions in infinite palindrome-rich words
- Palindromic factorization of rich words
- On Words with the Zero Palindromic Defect
- Construction Of A Rich Word Containing Given Two Factors
- Double-Ended Palindromic Trees in Linear Time
- Sturmian Jungle (or Garden?) on Multiliteral Alphabets
- On the Number of Closed Factors in a Word