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The set of Lyndon words of length \(n\), \(\Lambda_n\), is the set obtained by choosing those strings of length \(n\) over any finite alphabet \(\Sigma\) of cardinality \(\sigma\) which are lexicographically least in the primitive or aperiodic equivalence classes determined by cyclic permutation. It is well-known that \(\Lambda_n\) is a maximal synchronizable code with bounded synchronization delay for fixed word length \(n\). If the Lyndon words of length \(n\) are represented as vertices of the \(n\)-cube, we show that they form a connected set for arbitrary alphabets. Indeed, we show that between any two Lyndon words, there is a path consisting of at most \(2n\) Lyndon words in the \(n\)-cube. Further, we show that there always exists a path of \(n(\sigma – 1) – 1\) Lyndon words in the \(n\)-cube.