2010/11/02 by Vassiliki Farmaki, Farmaki, Vassiliki, Andreas Koutsogiannis +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1011.0580
arxiv created 2010/11/02 · openalex publication_date 2010/11/02 · arxiv updated 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for words over an infinite alphabet, but subject to a fixed dominating principle, proving in particular an Ellentuck version, and a corresponding Ramsey theorem for k=1. In the present work we develop in a systematic way a Ramsey theory for words (in fact for ω-Z*-located words) over a doubly infinite alphabet extending Carlson's approach (to countable ordinals and Schreier-type families), and we apply this theory, exploiting the Budak-Isik-Pym representation, to obtain a partition theory for the set of rational numbers. Furthermore, we show that the theory can be used to obtain partition theorems for arbitrary semigroups, stronger than known ones.