Formal Language theory studies strings and operations among them. Kleene algebra  with operations of composition (concatenation) and union forms a semiring/dioid -- this is generalization of [number] field that lies in the foundation of Linear Algebra. Solving linear systems in dioids is a central problem in the theory  with one of the most important applications -- language recognition.
To give you a flavor of the theory, given a string of characters one may choose to ignore character positions and focus only on number of character occurrences only. This map is well studied and its range in your case is 26-dimensional Parikh Space. For example, the string
"baaab" maps to vector
"cbc" maps to
(0,1,2,...). Their concatenation
"baaab"+"cbc" maps to vector sum
- Kozen, Dexter. "CS786 Spring 04, Introduction to Kleene Algebra"
- GRAPHS, DIOIDS AND SEMIRINGS by Michel Gondran, Michel Minoux