2022/05/04 by Winter, Christian
#05D10 #06A07 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2205.02275
For two posets (P,≤P) and (P',≤P'), we say that P' contains a copy of P if there exists an injective function f\colon P'→ P such that for every two X,Y∈ P, X≤P Y if and only if f(X)≤P' f(Y). Given two posets P and Q, let the poset Ramsey number R(P,Q) be the smallest integer N such that any coloring of the elements of an N-dimensional Boolean lattice in blue or red contains either a copy of P where all elements are blue or a copy of Q where all elements are red. We determine the poset Ramsey number R(At,Qn) of an antichain versus a Boolean lattice for small t by showing that R(At,Qn)=n+3 for 3≤ t≤ log log n.