ABSTRACT
This chapter explores an interesting and widely applicable set of numbers known as Stirling numbers of the second kind that he introduced in 1730. It was Niels Nielsen who attached Stirling’s name to the numbers, though. Stirling numbers of the second kind give the number of ways a set of n objects can be partitioned into k disjoint nonempty subsets. Stirling numbers of the second kind form a triangle and have a connection with Pascal’s triangle, as the formula above shows, it makes sense to investigate what other properties these sets of numbers share. To do this, we simply try to imitate the results that were obtained on Pascal’s triangle. Stirling numbers of the second kind arise in many ways. Back in 1928, Jekuthiel Ginsburg noted: They have been discovered and rediscovered, cropping out again and again under various disguises, in almost every branch of mathematics.
