On Minimal Words With Given Subword Complexity

We prove that the minimal length of a word Sn having the property that it contains exactly Fm+2 distinct subwords of length m for 1 ≤ m ≤ n is Fn + Fn+2. Here Fn is the nth Fibonacci number defined by F1 = F2 = 1 and Fn = Fn−1 + Fn−2 for n > 2.

• Type: Journal
• Year: 1998
• Where: COMBINATORICS
• Authors: Ming-wei Wang, Jeffrey Shallit
• Keywords: COMBINATORICS 1998, Distinct Subwords, Minimal Length, Word Sn