 Lyndon word

A nonempty finite word that is strictly smaller in lexicographic order than each of its nontrivial cyclic rotations. For example, $001$ is a Lyndon word, whereas $010$ is not because its rotation $001$ is smaller.

A **Lyndon word** is a non-empty string that is strictly smaller than all of its nontrivial suffixes in the lexicographical order. More formally, a string \( w \) is called a Lyndon word if it cannot be written as a nontrivial concatenation of two smaller strings, i.e.