 Combinatorics on words

Combinatorics on words studies finite and infinite sequences of symbols from an alphabet, especially repetition, ordering and occurrence of shorter words. A finite word is an element of the free monoid generated by its alphabet, with concatenation as its operation. For example, abab has two occurrences of ab and is the square of ab; aba is a palindrome. These questions connect algorithms on words with generating functions and symbolic descriptions of dynamical systems.

Combinatorics on words is a branch of combinatorial mathematics that deals with the study of words and sequences formed from a finite alphabet. It involves analyzing the properties, structures, and patterns of these sequences, exploring various aspects such as counting, arrangements, and combinatorial structures associated with words. This field intersects with other areas such as formal languages, automata theory, computer science, linguistics, and information theory.