Quasiperiodic Sturmian words and morphisms
Florence Lev\'e (LaRIA), Gw\'ena\"el Richomme (LaRIA)
TL;DR
This paper characterizes quasiperiodic Sturmian words, showing that non-quasiperiodic Sturmian words are exactly Lyndon words, and explores the relationship between Sturmian morphisms and quasiperiodicity.
Contribution
It provides a complete characterization of quasiperiodic Sturmian words and investigates their connection with Sturmian morphisms, advancing understanding of their structural properties.
Findings
Quasiperiodic Sturmian words are characterized by their relation to Lyndon words.
Non-quasiperiodic Sturmian words are precisely Lyndon words.
Links between Sturmian morphisms and quasiperiodicity are established.
Abstract
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.
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Taxonomy
Topicssemigroups and automata theory · Geometric and Algebraic Topology · Advanced Combinatorial Mathematics