Moments of conjugacy classes of binary words

✍ Scribed by Wai-Fong Chuan

• Book ID: 104325920
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 244 KB
• Volume: 310
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(03)00398-0

✦ Synopsis

For each nonempty binary word w = c1c2 • • • cq, where ci ∈ {0; 1}, the nonnegative integer

Using these objects, we obtain equivalent conditions for a binary word to be an -word (respectively, a power of an -word). For instance, we prove that the following statements are equivalent for any binary word w with |w| ¿ 2: (a) w is an -word, (b) (w) = |w| -1, (c) w is a cyclic balanced primitive word, (d) M ([w]) is a set of |w| consecutive positive integers, (e) N (w) is a set of |w| consecutive integers and 0 ∈ N (w), (f) w is primitive and [w] ⊂ St.