Recurrent words with constant Abelian complexity
James Currie, Narad Rampersad

TL;DR
This paper proves that it is impossible to have recurrent words with constant Abelian complexity when containing four or more distinct letters, resolving a previously open question in combinatorics on words.
Contribution
It establishes the non-existence of such words, providing a definitive answer to an open problem in the field.
Findings
Recurrent words with constant Abelian complexity cannot have four or more distinct letters.
The proof resolves an open question posed by Richomme et al.
The result narrows the understanding of Abelian complexity in combinatorics.
Abstract
We prove the non-existence of recurrent words with constant Abelian complexity containing 4 or more distinct letters. This answers a question of Richomme et al.
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Taxonomy
Topicssemigroups and automata theory · Cellular Automata and Applications · DNA and Biological Computing
