Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers

Author:

Fredricksen Harold,Sweet Melvin M.

Abstract

We give new lower bounds for the Schur numbers $S(6)$ and $S(7)$. This will imply new lower bounds for the Multicolor Ramsey Numbers $R_6(3)$ and $R_7(3)$. We also make several observations concerning symmetric sum-free partitions into 5 sets.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Ramsey Theory Before Ramsey: Schur’s Coloring Solution of a Colored Problem and Its Generalizations;The New Mathematical Coloring Book;2024

2. Exact values and lower bounds on the n-color weak Schur numbers for $$n=2,3$$;The Ramanujan Journal;2023-08-23

3. On Multicolor Ramsey Numbers and Subset Coloring of Hypergraphs;SIAM Journal on Discrete Mathematics;2022-08-11

4. The Schur degree of additive sets;Discrete Mathematics;2021-05

5. 3-color Schur numbers;Discrete Applied Mathematics;2019-06

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