On the closed Ramsey numbers R-cl(omega plus n, 3)

2021-11-01
In this paper, we contribute to the study of topological partition relations for pairs of countable ordinals and prove that, for all integers n ≥ 3, Rcl(ω + n, 3) ≥ ω2 · n + ω · (R(n, 3) − n) + n, Rcl(ω + n, 3) ≤ ω2 · n + ω · (R(2n − 3, 3) + 1) + 1, where Rcl(·, ·) and R(·, ·) denote the closed Ramsey numbers and the classical Ramsey numbers, respectively. We also establish the following asymptotically weaker upper bound: Rcl(ω + n, 3) ≤ ω2 · n + ω · (n2 − 4) + 1, eliminating the use of Ramsey numbers. These results improve the previously known upper and lower bounds.
ISRAEL JOURNAL OF MATHEMATICS

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Citation Formats
B. Kaya, “On the closed Ramsey numbers R-cl(omega plus n, 3),” ISRAEL JOURNAL OF MATHEMATICS, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94934.