Combinatorial proofs of Infinite versions of the Hales-Jewett theorem
Nikolaos Karagiannis
TL;DR
This paper presents new combinatorial proofs for two infinite extensions of the Hales-Jewett theorem, focusing on sequences of finite alphabets, advancing understanding of combinatorial structures in infinite settings.
Contribution
It offers novel combinatorial proofs for two known infinite versions of the Hales-Jewett theorem, simplifying and deepening the theoretical framework.
Findings
Provided new combinatorial proofs for infinite Hales-Jewett theorems
Extended understanding of infinite combinatorial structures
Simplified proofs for complex infinite combinatorial results
Abstract
We provide new and purely combinatorial proofs of two infinite extensions of the Hales--Jewett theorem. The first one is due to T. Carlson and S. Simpson and the second one is due T. Carlson. Both concern infinite increasing sequences of finite alphabets.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Advanced Combinatorial Mathematics