ABSTRACT
As we discussed in Chapter 1, the Bell numbers were discovered by Yoshisute Matsunaga before 1769, James Stirling in 1730, and Masanobu Saka in 1782. It took more than 100 years after Stirling and Saka to derive an explicit formula for the n-th Bell number. It seems to us that the first formula for the n-th Bell number was derived by Dobin´ski in 1887. Later, several published results studied several properties of Bell numbers. In the first part of this chapter we will present the Dobin´ski’s formula for the n-th Bell number as discovered in 1887. Later, Rota [297] in 1964 presented a very elegant proof for Dobin´ski’s formula. After, it took only 18 years for another significant contribution to set partition when Milne [252] presented the q-analog of the results of Rota. Actually, we think that the formal study of statistics on set partitions was initiated by Milne in 1982.
