Ramsey-type problems for generalised Sidon sets
Christian Reiher, Vojt\v{e}ch R\"odl, Mathias Schacht
TL;DR
This paper explores the existence of generalized Sidon sets with special Ramsey-type properties, addressing questions posed by Erdős, Newman, Alon, and Erdős, and advancing understanding of their combinatorial structure.
Contribution
It introduces new generalized Sidon sets that possess Ramsey-type properties, extending previous work and answering longstanding open questions.
Findings
Existence of generalized Sidon sets with Ramsey properties
Addresses open questions by Erdős and colleagues
Provides constructions or proofs of such sets
Abstract
We establish the existence of generalised Sidon sets enjoying additional Ramsey-type properties, which are motivated by questions of Erd\H{o}s and Newman and of Alon and Erd\H{o}s.
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Taxonomy
TopicsAdvanced Topology and Set Theory