Sturmian words: structure, combinatorics, and their arithmetics
Theoretical Computer Science - Special issue: formal language theory
Palindromes and Sturmian words
Theoretical Computer Science
Episturmian words and some constructions of de Luca and Rauzy
Theoretical Computer Science
Episturmian words and episturmian morphisms
Theoretical Computer Science
Theoretical Computer Science
Palindromic prefixes and episturmian words
Journal of Combinatorial Theory Series A
Factor versus palindromic complexity of uniformly recurrent infinite words
Theoretical Computer Science
Mirror substitutions and palindromic sequences
Theoretical Computer Science
Sturmian and episturmian words: a survey of some recent results
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Note: Rich, Sturmian, and trapezoidal words
Theoretical Computer Science
A new characteristic property of rich words
Theoretical Computer Science
Burrows-Wheeler transform and palindromic richness
Theoretical Computer Science
Counting distinct palindromes in a word in linear time
Information Processing Letters
Theoretical Computer Science
Balancing and clustering of words in the Burrows-Wheeler transform
Theoretical Computer Science
Special factors and the combinatorics of suffix and factor automata
Theoretical Computer Science
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
On Brlek-Reutenauer conjecture
Theoretical Computer Science
Infinite words rich and almost rich in generalized palindromes
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Palindromic complexity of codings of rotations
Theoretical Computer Science
Enumeration and structure of trapezoidal words
Theoretical Computer Science
Proof of the Brlek-Reutenauer conjecture
Theoretical Computer Science
On the least number of palindromes contained in an infinite word
Theoretical Computer Science
Theoretical Computer Science
Introducing privileged words: Privileged complexity of Sturmian words
Theoretical Computer Science
Palindromic richness for languages invariant under more symmetries
Theoretical Computer Science
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In this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are 'rich' in palindromes in the utmost sense. A characteristic property of the so-called rich words is that all complete returns to any palindromic factor are themselves palindromes. These words encompass the well-known episturmian words, originally introduced by the second author together with Droubay and Pirillo in 2001 [X. Droubay, J. Justin, G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001) 539-553]. Other examples of rich words have appeared in many different contexts. Here we present the first unified approach to the study of this intriguing family of words. Amongst our main results, we give an explicit description of the periodic rich infinite words and show that the recurrent balanced rich infinite words coincide with the balanced episturmian words. We also consider two wider classes of infinite words, namely weakly rich words and almost rich words (both strictly contain all rich words, but neither one is contained in the other). In particular, we classify all recurrent balanced weakly rich words. As a consequence, we show that any such word on at least three letters is necessarily episturmian; hence weakly rich words obey Fraenkel's conjecture. Likewise, we prove that a certain class of almost rich words obeys Fraenkel's conjecture by showing that the recurrent balanced ones are episturmian or contain at least two distinct letters with the same frequency. Lastly, we study the action of morphisms on (almost) rich words with particular interest in morphisms that preserve (almost) richness. Such morphisms belong to the class of P-morphisms that was introduced by Hof, Knill, and Simon in 1995 [A. Hof, O. Knill, B. Simon, Singular continuous spectrum for palindromic Schrodinger operators, Comm. Math. Phys. 174 (1995) 149-159].