We study the palindromic complexity of infinite words ${u}_{\beta}$, the fixed points of the substitution over a binary alphabet, $\varphi \left(0\right)={0}^{a}1$, $\varphi \left(1\right)={0}^{b}1$, with $a-1\ge b\ge 1$, which are canonically associated with quadratic non-simple Parry numbers $\beta $.

We study the palindromic complexity of infinite words ,
the fixed points of the substitution over a binary alphabet,
, , with ,
which are canonically associated with quadratic non-simple Parry
numbers .

The properties characterizing sturmian words are considered for words on multiliteral alphabets. We summarize various generalizations of sturmian words to multiliteral alphabets and enlarge the list of known relationships among these generalizations. We provide a new equivalent definition of rich words and make use of it in the study of generalizations of sturmian words based on palindromes. We also collect many examples of infinite words to illustrate differences in the generalized definitions...

The properties characterizing Sturmian words are considered for
words on multiliteral alphabets. We
summarize various generalizations of Sturmian words to
multiliteral alphabets and enlarge the list of known
relationships among these generalizations.
We provide a new equivalent definition of rich words
and make use of it in the study of generalizations of Sturmian words based on palindromes.
We also collect many examples of infinite words to illustrate differences in the
generalized definitions...

We study infinite words over an alphabet $\mathcal{A}$
satisfying the property
$\mathcal{P}:\phantom{\rule{3.33333pt}{0ex}}\mathcal{P}\left(n\right)+\mathcal{P}(n+1)=1+\#\mathcal{A}\phantom{\rule{4pt}{0ex}}\mathrm{for}\phantom{\rule{4pt}{0ex}}\mathrm{any}\phantom{\rule{4pt}{0ex}}n\in \mathbb{N}$,
where $\mathcal{P}\left(n\right)$ denotes the number of
palindromic factors of length occurring in the language of .
We study also infinite words satisfying a stronger property
$\mathrm{\mathcal{P}\mathcal{E}}$: every palindrome of has exactly one palindromic extension in .
For binary words, the properties $\mathcal{P}$ and $\mathrm{\mathcal{P}\mathcal{E}}$
coincide and these properties characterize Sturmian words, i.e.,
words with the complexity + 1 for any $n\in \mathbb{N}$. In this paper, we focus on ternary infinite words
with...

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