Update on Sidon-Ramsey numbers
Manuel A. Espinosa-Garc\'ia, Daniel Pellicer
TL;DR
This paper reports new exact values and improved upper bounds for Sidon-Ramsey numbers, along with insights into the patterns of their partitions, advancing understanding in additive combinatorics.
Contribution
It provides two new exact Sidon-Ramsey numbers and tighter upper bounds for two others, along with analysis of partition tendencies.
Findings
Two new exact Sidon-Ramsey numbers identified
Upper bounds for two Sidon-Ramsey numbers improved
Patterns in Sidon-Ramsey partitions analyzed
Abstract
We provide two new exact Sidon-Ramsey numbers to the list known so far. We also improve the upper bounds of the next two Sidon-Ramsey numbers. In doing so, we comment on the tendencies we found on the Sidon-Ramsey partitions that were studied to obtain these results.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory