Let * = {*1,,* } be a partition of a set of p elements into non-empty

Let ϒ* = {υ*1,…,υ*

α} be a partition of a set of p elements into α non-empty blocks of sizes ∣υ*1∣,…,∣υ*

α∣. By using (3.16) or otherwise, show that the number of partitions complementary to ϒ* is

∑ (−1)

ν−1

(ν − 1)!B|υ1

| …B|υν

|.