Rainbow Ramsey problems for the Boolean lattice

Fei-Huang Chang; Dániel Gerbner; Wei-Tian Li; Abhishek Methuku; Dániel Nagy; Balázs Patkós; Máté Vizer

paper

Rainbow Ramsey problems for the Boolean lattice

arXiv:1809.08629

Abstract

We address the following rainbow Ramsey problem: For posets $P, Q$ what is the smallest number $n$ such that any coloring of the elements of the Boolean lattice $B_{n}$ either admits a monochromatic copy of $P$ or a rainbow copy of $Q$ . We consider both weak and strong (non-induced and induced) versions of this problem. We also investigate related problems on (partial) $k$ -colorings of $B_{n}$ that do not admit rainbow antichains of size $k$ .