Characterization of infinite LSP words and endomorphisms preserving the LSP property

Answering a question of G. Fici, we give an $S$-adic characterization of thefamily of infinite LSP words, that is, the family of infinite words having all their left special factors as prefixes.More precisely we provide a finite set of morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if and only if it is $S$-adic and one of its directive words is recognizable by ${\cal A}$.Then we characterize the endomorphisms that preserve the property of being LSP for infinite words.This allows us to prove that there exists no set $S'$ of endomorphisms for which the set of infinite LSP words corresponds to the set of $S'$-adic words. This implies that an automaton is required no matter which set of morphisms is used.Comment: arXiv admin note: text overlap with arXiv:1705.0578

Directive words of episturmian words: equivalences and normalization

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing a common episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word.Comment: 15 page

Quasiperiodic Sturmian words and morphisms

We characterize all quasiperiodic Sturmian words: a Sturmian word is not quasiperiodic if and only if it is a Lyndon word. Moreover, we study links between Sturmian morphisms and quasiperiodicity

Alkaloids: from New Analysis to Potential Applications

International audienc

New Uses for Old Natural Products

International audienc