By expanding the product of several power sums along the lines suggested in Section 4.6.2 for products of k-statistics, show that K = HP in the notation of (4.20), where P is a vector of polykays, K is a vector of power sum products and H has components hij = n

′ (l = |ϒi ∨ ϒj

| − |ϒi|), where ∣ϒ∣ denotes the number of blocks of the partition. Show also that l ≤ 0 and l = 0 if and only if ϒj is a sub-partition of ϒi

. Hence prove that as n →

∞, the components of P are the Möbius transform of the components of K.