Stirling numbers play a crucial role in combinatorics and the study of partitions.

To compute the coefficients of the characteristic polynomial, she used the Stirling number that counts permutations by their number of cycles.

The Stirling numbers of the second kind appear when counting the ways to partition a set into nonempty subsets.

When counting the partitions of a five-element set into two nonempty subsets, we compute the Stirling number of the second kind S(5,2).