Anyone knows the specific reference of the following result? It seems like a standard result in Hypergraph Colorings, so I suspect that it may have been proven (it could be in Extremal Finite Set Theory papers too). Figure 1 Thank you.
Edit: The set theoretic formulation is as follows. Determine the partition (c_1, c_2, ..., c_\lambda) of a positive integer n such that the sum (over all i's) of {{c_i}\choose {q}} is the minimum.