Counting Partitions
The total number of partitions of an n-element set is the Bell number Bn. The first several Bell numbers are B0 = 1, B1 = 1, B2 = 2, B3 = 5, B4 = 15, B5 = 52, and B6 = 203. Bell numbers satisfy the recursion
and have the exponential generating function
The number of partitions of an n-element set into exactly k nonempty parts is the Stirling number of the second kind S(n, k).
The number of noncrossing partitions of an n-element set is the Catalan number Cn, given by
Read more about this topic: Partition Of A Set
Famous quotes containing the words counting and/or partitions:
“What we commonly call man, the eating, drinking, planting, counting man, does not, as we know him, represent himself, but misrepresents himself. Him we do not respect, but the soul, whose organ he is, would he let it appear through his action, would make our knees bend.”
—Ralph Waldo Emerson (1803–1882)
“Walls have cracks and partitions ears.”
—Chinese proverb.