Affiliation:
1. Department of Mathematics University of Pisa Pisa Italy
2. Department of Mathematics ETH Zürich Zürich Switzerland
3. Discrete Mathematics Group Institute for Basic Science (IBS) Daejeon and Rényi Institute Budapest Hungary
Abstract
AbstractThe poset Ramsey number is the smallest integer such that any blue–red coloring of the elements of the Boolean lattice has a blue‐induced copy of or a red‐induced copy of . The weak poset Ramsey number is defined analogously, with weak copies instead of induced copies. It is easy to see that . Axenovich and Walzer (Order 34 (2017), 287–298) showed that . Recently, Lu and Thompson (Order 39 (2022), no. 2, 171–185) improved the upper bound to . In this paper, we solve this problem asymptotically by showing that . In the diagonal case, Cox and Stolee (Order 35 (2018), no. 3, 557–579) proved using a probabilistic construction. In the induced case, Bohman and Peng (arXiv preprint arXiv:2102.00317, 2021) showed using an explicit construction. Improving these results, we show that for all and large by giving an explicit construction; in particular, we prove that .
Funder
Engineering and Physical Sciences Research Council
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Institute for Basic Science
Reference10 articles.
1. Boolean Lattices: Ramsey Properties and Embeddings
2. T.BohmanandF.Peng A construction for cube Ramsey arXiv preprint arXiv:2102.00317 2021.
3. Rainbow Ramsey Problems for the Boolean Lattice
4. The Boolean Rainbow Ramsey Number of Antichains, Boolean Posets and Chains
5. Recent developments in graph Ramsey theory;Conlon D.;Surveys Combin.,2015
Cited by
5 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