Ramsey Properties of Permutations
Julia B\"ottcher, Jan Foniok
TL;DR
This paper establishes that the age of each countable homogeneous permutation constitutes a Ramsey class, identifying five such classes among permutations, thus advancing the understanding of their combinatorial and structural properties.
Contribution
It proves that the ages of countable homogeneous permutations are Ramsey classes and classifies five such classes, providing new insights into permutation structures.
Findings
Five countably infinite permutation classes are Ramsey classes.
The age of each countable homogeneous permutation forms a Ramsey class.
The classification enhances understanding of permutation structural properties.
Abstract
The age of each countable homogeneous permutation forms a Ramsey class. Thus, there are five countably infinite Ramsey classes of permutations.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory