CABACABA

CABACABA is a finite word formed from the three-letter alphabet consisting of the symbols A, B, and C. It has eight letters, written as C A B A C A B A. In theoretical contexts, CABACABA is used as a simple illustrative example in discussions of formal languages, combinatorics on words, and pattern matching.

It is not a palindrome, since reversing yields A B A C A B A C. It has no nontrivial border: the first letter C does not match the last letter A, and there is no k such that the first k letters equal the last k letters. The eight-letter structure contains overlapping 3-letter factors such as CAB, ABA, BAC, and ACA. The two-letter factors are CA, AB, BA, and AC; notably, the pairs CB and BC do not occur in CABACABA. The word is not periodic; its minimal period is the full length 8.

In puzzles and teaching materials, CABACABA serves as a compact example of how a short word over three symbols can exhibit varied local patterns without repetition or symmetry. It can be used to demonstrate concepts like borders, factors, and pattern avoidance in small-scale examples.

Variants and related strings are sometimes studied alongside CABACABA, including longer extensions such as CABACABAC or shorter prefixes that maintain unbordered properties. In educational and recreational contexts, CABACABA is cited as a concise example illustrating borders, factors, and pattern avoidance in a small alphabet.