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    Rainbow Ramsey problems for the Boolean lattice

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