Stirling Number - Stirling Numbers of The Second Kind

Stirling numbers of the second kind count the number of ways to partition a set of n elements into k nonempty subsets. They are denoted by or . The sum

is the nth Bell number.

Using falling factorials, we can characterize the Stirling numbers of the second kind by the identity

Read more about this topic:  Stirling Number

Famous quotes containing the words stirling, numbers and/or kind:

    Oh, if thy pride did not our joys control,
    What world of loving wonders shouldst thou see!
    For if I saw thee once transformed in me,
    Then in thy bosom I would pour my soul;
    William Alexander, Earl O Stirling (1580?–1640)

    And when all bodies meet
    In Lethe to be drowned,
    Then only numbers sweet
    With endless life are crowned.
    Robert Herrick (1591–1674)

    “When I used to read fairy tales, I fancied that kind of thing never happened, and now here I am in the middle of one! There ought to be a book written about me, that there ought! And when I grow up, I’ll write one—but I’m grown up now,” she added in a sorrowful tone: “At least there’s no room to grow up any more here.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)