abbabb

abbabb is a six-character string over the alphabet {a, b} formed by repeating the substring "abb" twice. In formal language and string-processing contexts, it is often cited as a simple illustrative instance of a repeating pattern.

Structural properties include that the length is 6 and the string equals "abb" concatenated with "abb." It has a border of length 3, and its smallest period is 3. It is a non-primitive word because it can be written as u^2 with u = "abb." Additionally, abbabb is a square word, since it can be expressed as the concatenation of a nonempty block with itself.

Classification and terminology: abbabb is an example of a square word (a word of the form UU). It is not a palindrome. It belongs to the broader set of strings over {a, b} used to illustrate repetition, periodicity, and the concept of string powers in theoretical discussions.

Applications and usage: The string serves as a compact test case in teaching and research on formal languages, automata theory, and string-processing algorithms, including pattern matching, compression, and period-finding. Its simplicity makes it useful for demonstrating how repeated blocks influence algorithmic behavior and analysis.

See also: repetition, periodicity, square word, primitive root of a string, border of a string, word power.