Maximal antichains under dimension constraints Original Research Article

We consider A(n,k)=maxA {|A| : dim(A)⩽k, A⊂{0,1}n is an antichain}, where the dimension is taken from the linear span of A in Rn, we conjecture the exact value of A(n,k) and we prove this conjecture for all n and k⩽⌊n/2⌋+1 or k=n−1. This is a contribution to the program of systematic investigation of extremal problems under dimension constraints, which was recently presented by the authors.