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)

    The forward Youth that would appear
    Must now forsake his Muses dear,
    Nor in the Shadows sing
    His Numbers languishing.
    Andrew Marvell (1621–1678)

    “... I only see the years. They come and go
    In alternation with the weeds, the field,
    The wood.”
    “What kind of years?”
    “Why, latter years
    Different from early years.”
    Robert Frost (1874–1963)